(CNN) Hillary Clinton showed up at the debate of the century and delivered.

Donald Trump started out strong, then struggled.

The Democratic and Republican nominees waged a fiery battle Monday night when they appeared on stage together for the first time -- a clash of two famous personalities locked in a dead heat for the presidency. During one of the most highly anticipated debates in modern political history, the candidates drew sharp contrasts on temperament, character and policy and starkly different visions of where they would lead the nation.

Clinton had the better night, repeatedly putting the Republican nominee on defense on the issues most likely to damage his White House campaign -- his refusal to release his taxes, his past comments on race and his attitude toward women.

By Tuesday morning, Clinton knew she came out on top. During a gaggle with reporters on her plane, Clinton taunted Trump's complaint that the microphone at his podium was "defective."

"Anybody who complains about the microphone is not having a good night."

Trump started out strong and made effective points on the economy, trade and jobs that were uncomfortable at times for his rival. He put Clinton in a tight spot as he repeatedly accused her of being in Washington for 30 years and of doing little to improve the economic health of Americans, a line that could resonate in key swing states such as Pennsylvania and Ohio.

Photos: The first presidential debate Photos: The first presidential debate Republican presidential nominee Donald Trump shakes hands with Democratic presidential nominee Hillary Clinton at the first presidential debate on Monday, September 26. Hide Caption 1 of 21 Photos: The first presidential debate NBC's Lester Holt moderated the debate, which was held at Hofstra University in Hempstead, New York. Hide Caption 2 of 21 Photos: The first presidential debate The debate took place 43 days before Election Day. There are two more debates scheduled. Hide Caption 3 of 21 Photos: The first presidential debate Clinton, 68, is the first woman to lead a presidential ticket for one of the major political parties. She has been a U.S. senator and secretary of state. Hide Caption 4 of 21 Photos: The first presidential debate This was the first one-on-one debate for Trump, a billionaire real estate developer and neophyte politician. The 70-year-old has shattered every rule and convention in politics with his stunning presidential campaign. Hide Caption 5 of 21 Photos: The first presidential debate Clinton is clinging to a narrow lead in many national polls, but she now has almost no margin of error in the battleground states that will decide who will take the oath of office in January. Hide Caption 6 of 21 Photos: The first presidential debate Trump has been picking up momentum lately in the polls. CNN's Poll of Polls finds Clinton and Trump neck-and-neck nationally, with Clinton leading 44%-42%. Hide Caption 7 of 21 Photos: The first presidential debate Clinton answers a question during the debate. Hide Caption 8 of 21 Photos: The first presidential debate The candidates clashed repeatedly over the economy, tax cuts for the wealthy and ISIS. Hide Caption 9 of 21 Photos: The first presidential debate Trump smiles during the debate. Hide Caption 10 of 21 Photos: The first presidential debate Clinton smiles during the debate. Hide Caption 11 of 21 Photos: The first presidential debate Trump and Clinton shake hands before the start of the debate. Hide Caption 12 of 21 Photos: The first presidential debate The debate was attracting worldwide interest, with a television audience expected to approach 100 million. Hide Caption 13 of 21 Photos: The first presidential debate Clinton waves to the crowd after shaking hands with Trump. Hide Caption 14 of 21 Photos: The first presidential debate Trump's wife, Melania, shakes hands with Clinton's husband, former U.S. President Bill Clinton. Hide Caption 15 of 21 Photos: The first presidential debate From left, in the front row, are Melania Trump; Trump's daughter Ivanka Trump; Trump's running mate, Indiana Gov. Mike Pence; Pence's wife, Karen; retired U.S. Army Gen. Michael Flynn; and former New York Mayor Rudy Giuliani. Hide Caption 16 of 21 Photos: The first presidential debate Bill Clinton, sitting next to daughter Chelsea, waves to the audience before the debate. Hide Caption 17 of 21 Photos: The first presidential debate The crowd was urged to stay quiet throughout the debate, but there was occasional applause and laughs. Hide Caption 18 of 21 Photos: The first presidential debate Trump and Clinton face off in the debate. Hide Caption 19 of 21 Photos: The first presidential debate Clinton is seen on television monitors in the media center at Hofstra. Hide Caption 20 of 21 Photos: The first presidential debate Trump appears on the media center screens. Hide Caption 21 of 21

But he appeared to fade as the night wore on, failing to effectively press Clinton on her deepest vulnerabilities on her private emails server and long history of ethical questions.

The debate, at Hofstra University on New York's Long Island, came at a critical point of the campaign: Trump has grabbed momentum in national polls and narrowed the race in some of the most decisive swing states. The debate had the potential for him to build on that momentum with 42 days remaining before Election Day.

First signs positive for Clinton

But the first results indicated that Clinton won. A CNN/ORC poll after the clash showed Clinton had a commanding victory, by 62% to 27%. The poll suggested the debate audience was a bit more Democratic than the public as a whole, about on par with the Democratic tilt in the audience that watched the first debate in 2008 between Barack Obama and John McCain.

In all, 68% of those asked said Clinton had a better understanding of the issues, while 27% said the same of Trump. Asked whether Trump could handle the presidency, 55% said no.

It will be several days, however, until conventional wisdom about the result of the showdown gels and its impact on the campaign becomes evident. Trump appeared to do nothing to shake the strong faith in his campaign among his core supporters, though the Republican nominee may have failed to broaden his coalition among key voting blocks, minorities and women.

The showdown came at a critical point in the race. Another CNN/ORC poll released Monday found Trump edging Clinton 42% to 41% in the crucial battleground state of Colorado among likely voters in a four-way race. In Pennsylvania, another key state, the poll found Clinton in a virtual tie against Trump among likely voters at 45% to 44%.

The former secretary of state is relying on both states to help pave her way to the 270 electoral votes needed to win the White House.

Nationally, CNN's Poll of Polls finds Clinton and Trump neck-and-neck 44%-42%.

Both candidates clearly understood that the central question of Monday's debate was about who had the right temperament and character to serve as President of the United States. Clinton delivered the best zinger of the night in response to criticism from Trump for staying off the campaign trail recently.

"I think Donald just criticized me for preparing for this debate," she said. "And yes, I did. And you know what else I prepared for? I prepared to be President. And that is a good thing."

Trump's falsehoods

Clinton also repeatedly brought attention to Trump's reputation for spreading falsehoods and repeatedly tried to needle him, at one point blasting his "trumped up, trickle down" economics.

Trump, however, said he was much better suited to the burdens of the Oval Office.

"I have a winning temperament, I know how to win. She does not know how to win," he said.

The billionaire skewered Clinton on her past support for the Trans Pacific Partnership (TPP) trade deal, which she declared the "gold standard" when she was secretary of state but now opposes.

Clinton's team was clearly delighted with their candidate's performance, declaring her the clear winner. Trump appeared in the "spin room" as soon as the 90 minute debate was over, telling CNN's Dana Bash "it went better than I ever thought." He also told reporters his microphone wasn't working and questioned whether that was happening on purpose.

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Often in presidential debates, the atmospherics and body language are as important to winning over undecided voters as what the candidates say. On that score, Clinton went out of her way to appear unruffled and calm. She often responded to Trump's attacks with smiles and laughs. She pointedly repeatedly referred to Trump as "Donald" -- in an apparent bid to cut him down to size, not using the moniker "Mr. Trump" that he prefers.

Trump, while passionate and engaged, also appeared to play into concerns about his personality. He often spoke loudly over Clinton in a way that could have come across as condescending, apparently falling short of his goal to appear more presidential than his rival.

Monday's event was Trump's first ever one-on-one political debate -- and he has two more showdowns with Clinton to change the political narrative before the election. There have been several instances of candidates recovering from an underwhelming first debate to recapture momentum and win the presidency in November.

Powerful moments

One of the most powerful moments of the debate came when the conversation focused on the so-called birther debate following Trump's recent acknowledgment that President Barack Obama was born in the US -- a fact that has been evident for years. With Trump standing just a few feet from her, Clinton blasted him for perpetuating a "racist lie."

Photos: Donald Trump's rise Photos: Donald Trump's rise President-elect Donald Trump has been in the spotlight for years. From developing real estate and producing and starring in TV shows, he became a celebrity long before winning the White House. Hide Caption 1 of 37 Photos: Donald Trump's rise Trump at age 4. He was born in 1946 to Fred and Mary Trump in New York City. His father was a real estate developer. Hide Caption 2 of 37 Photos: Donald Trump's rise Trump, left, in a family photo. He was the second-youngest of five children. Hide Caption 3 of 37 Photos: Donald Trump's rise Trump, center, stands at attention during his senior year at the New York Military Academy in 1964. Hide Caption 4 of 37 Photos: Donald Trump's rise Trump, center, wears a baseball uniform at the New York Military Academy in 1964. After he graduated from the boarding school, he went to college. He started at Fordham University before transferring and later graduating from the Wharton School, the University of Pennsylvania's business school. Hide Caption 5 of 37 Photos: Donald Trump's rise Trump stands with Alfred Eisenpreis, New York's economic development administrator, in 1976 while they look at a sketch of a new 1,400-room renovation project of the Commodore Hotel. After graduating college in 1968, Trump worked with his father on developments in Queens and Brooklyn before purchasing or building multiple properties in New York and Atlantic City, New Jersey. Those properties included Trump Tower in New York and Trump Plaza and multiple casinos in Atlantic City. Hide Caption 6 of 37 Photos: Donald Trump's rise Trump attends an event to mark the start of construction of the New York Convention Center in 1979. Hide Caption 7 of 37 Photos: Donald Trump's rise Trump wears a hard hat at the Trump Tower construction site in New York in 1980. Hide Caption 8 of 37 Photos: Donald Trump's rise Trump was married to Ivana Zelnicek Trump from 1977 to 1990, when they divorced. They had three children together: Donald Jr., Ivanka and Eric. Hide Caption 9 of 37 Photos: Donald Trump's rise The Trump family, circa 1986. Hide Caption 10 of 37 Photos: Donald Trump's rise Trump uses his personal helicopter to get around New York in 1987. Hide Caption 11 of 37 Photos: Donald Trump's rise Trump stands in the atrium of the Trump Tower. Hide Caption 12 of 37 Photos: Donald Trump's rise Trump attends the opening of his new Atlantic City casino, the Taj Mahal, in 1989. Hide Caption 13 of 37 Photos: Donald Trump's rise Trump signs his second book, "Trump: Surviving at the Top," in 1990. Trump has published at least 16 other books, including "The Art of the Deal" and "The America We Deserve." Hide Caption 14 of 37 Photos: Donald Trump's rise Trump and singer Michael Jackson pose for a photo before traveling to visit Ryan White, a young child with AIDS, in 1990. Hide Caption 15 of 37 Photos: Donald Trump's rise Trump dips his second wife, Marla Maples, after the couple married in a private ceremony in New York in December 1993. The couple divorced in 1999 and had one daughter together, Tiffany. Hide Caption 16 of 37 Photos: Donald Trump's rise Trump putts a golf ball in his New York office in 1998. Hide Caption 17 of 37 Photos: Donald Trump's rise An advertisement for the television show "The Apprentice" hangs at Trump Tower in 2004. The show launched in January of that year. In January 2008, the show returned as "Celebrity Apprentice." Hide Caption 18 of 37 Photos: Donald Trump's rise A 12-inch talking Trump doll is on display at a toy store in New York in September 2004. Hide Caption 19 of 37 Photos: Donald Trump's rise Trump attends a news conference in 2005 that announced the establishment of Trump University. From 2005 until it closed in 2010, Trump University had about 10,000 people sign up for a program that promised success in real estate. Three separate lawsuits -- two class-action suits filed in California and one filed by New York's attorney general -- argued that the program was mired in fraud and deception. Trump's camp rejected the suits' claims as "baseless." And Trump has charged that the New York case against him is politically motivated. Hide Caption 20 of 37 Photos: Donald Trump's rise Trump attends the U.S. Open tennis tournament with his third wife, Melania Knauss-Trump, and their son, Barron, in 2006. Trump and Knauss married in 2005. Hide Caption 21 of 37 Photos: Donald Trump's rise Trump wrestles with "Stone Cold" Steve Austin at WrestleMania in 2007. Trump has close ties with the WWE and its CEO, Vince McMahon. Hide Caption 22 of 37 Photos: Donald Trump's rise For "The Apprentice," Trump was honored with a star on the Hollywood Walk of Fame in January 2007. Hide Caption 23 of 37 Photos: Donald Trump's rise Trump appears on the set of "The Celebrity Apprentice" with two of his children -- Donald Jr. and Ivanka -- in 2009. Hide Caption 24 of 37 Photos: Donald Trump's rise Trump poses with Miss Universe contestants in 2011. Trump had been executive producer of the Miss Universe, Miss USA and Miss Teen USA pageants since 1996. Hide Caption 25 of 37 Photos: Donald Trump's rise In 2012, Trump announces his endorsement of Republican presidential candidate Mitt Romney. Hide Caption 26 of 37 Photos: Donald Trump's rise Trump speaks in Sarasota, Florida, after accepting the Statesman of the Year Award at the Sarasota GOP dinner in August 2012. It was shortly before the Republican National Convention in nearby Tampa. Hide Caption 27 of 37 Photos: Donald Trump's rise Trump appears on stage with singer Nick Jonas and television personality Giuliana Rancic during the 2013 Miss USA pageant. Hide Caption 28 of 37 Photos: Donald Trump's rise In June 2015, during a speech from Trump Tower, Trump announced that he was running for President. He said he would give up "The Apprentice" to run. Hide Caption 29 of 37 Photos: Donald Trump's rise Trump -- flanked by U.S. Sens. Marco Rubio, left, and Ted Cruz -- speaks during a CNN debate in Miami on March 10. Trump dominated the GOP primaries and emerged as the presumptive nominee in May. Hide Caption 30 of 37 Photos: Donald Trump's rise The Trump family poses for a photo in New York in April. Hide Caption 31 of 37 Photos: Donald Trump's rise Trump speaks during a campaign event in Evansville, Indiana, on April 28. After Trump won the Indiana primary, his last two competitors dropped out of the GOP race. Hide Caption 32 of 37 Photos: Donald Trump's rise Trump delivers a speech at the Republican National Convention in July, accepting the party's nomination for President. "I have had a truly great life in business," he said. "But now, my sole and exclusive mission is to go to work for our country -- to go to work for you. It's time to deliver a victory for the American people." Hide Caption 33 of 37 Photos: Donald Trump's rise Trump faces Democratic nominee Hillary Clinton in the first presidential debate, which took place in Hempstead, New York, in September. Hide Caption 34 of 37 Photos: Donald Trump's rise Trump apologizes in a video, posted to his Twitter account in October, for vulgar and sexually aggressive remarks he made a decade ago regarding women. "I said it, I was wrong and I apologize," Trump said, referring to lewd comments he made during a previously unaired taping of "Access Hollywood." Multiple Republican leaders rescinded their endorsements of Trump after the footage was released. Hide Caption 35 of 37 Photos: Donald Trump's rise Trump walks on stage with his family after he was declared the election winner on November 9. "Ours was not a campaign, but rather, an incredible and great movement," he told his supporters in New York. Hide Caption 36 of 37 Photos: Donald Trump's rise Trump is joined by his family as he is sworn in as President on January 20. Hide Caption 37 of 37

"He has a long record of engaging in racist behavior," Clinton said as Trump shook his head.

Trump hit back, noting Clinton's tough critiques of Obama during their bitter 2008 primary battle.

"You treated him with terrible disrespect and I watch the way you talk now about how lovely everything is ... it doesn't work that way," he said. "When you try to act holier than thou, it really doesn't work."

As the debate ended, Clinton hammered Trump over his treatment of women.

"This is a man who has called women pigs, slobs and dogs," Clinton said.

She accused Trump of calling a Latina contestant in a beauty contest "Miss Piggy" and a housekeeper because of her ethnicity, seemingly throwing Trump off as he twice asked "Where did you find this?"

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He kept the story alive Tuesday morning when he slammed the contestant during an interview on "Fox and Friends."

"That person was a Miss Universe person. And she was the worst we ever had," Trump said. "She was the winner and you know, she gained a massive amount of weight and it was a real problem."

His comments recalled Trump's showdown with the family of fallen US Army captain Humayun Khan whose father had attacked him at the Democratic convention, prompting the Republican nominee to get into a damaging back and forth which prolonged the controversy.

During the debate, Clinton repeatedly sought to correct Trump's statements -- going so far as referring viewers to fact checks on her website -- as she aimed to portray him as out of touch with the complexities of the American economy.

"I know you live in your own reality," she told Trump.

Positive note

Clinton and Trump opened the debate on a positive note by shaking hands before stationing themselves behind their podiums. Their spouses, former President Bill Clinton and Melania Trump, also greeted each other before taking their seats in the debate hall.

From there, the drama quickly unfolded.

An increasingly angry Trump slammed Clinton for putting her plans to fight ISIS on her website -- and thereby tipping off America's enemy.

"Well, at least I have a plan to fight ISIS," Clinton responded, referring to his previous statements that he has a "secret" plan to destroy the terrorist group.

Battling over taxes

Clinton also hit Trump over his refusal to release his tax returns.

"Why won't he release his tax returns?" Clinton asked.

"Maybe he is not as rich as he says he is," she went on. "Maybe he is not as charitable as he claims to be. ... Maybe he doesn't want the American people to know that he has paid nothing in federal taxes."

Clinton pressed Trump on the issue, saying "There is something he is hiding."

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Trump replied that he would release his taxes when Clinton made public 33,000 emails that were deleted from her private email server. When Clinton said that Trump had paid no federal income tax in some years, Trump replied, "That makes me smart."

Clinton also set about Trump's business record, pointing out that he had called himself "The King of Debt" and accusing him of "stiffing" thousand of contractors who did work for his business.

When the debate turned to racial issues and crime, Clinton said that it was important for police to work together with local communities to restore trust.

Trump accused Clinton of refusing to say the phrase "law and order" and bemoaned the state of inner cities. He said that African-Americans and Hispanics were "living in hell."

"You walk down the street, you get shot," Trump said.

Clinton rebuked Trump for painting "such a dire picture" of black communities.