Washington (CNN) Hillary Clinton and Donald Trump won pivotal primaries Tuesday, while Gov. John Kasich's long-awaited debut victory in his home state of Ohio raised the chances of a historic GOP convention fight.

A humiliating loss on home ground in Florida, meanwhile, ended the White House dreams of Sen. Marco Rubio , who was once hailed as a Republican Party savior.

Clinton took big strides toward the Democratic nomination by winning Florida and North Carolina. And in crucial victories, she stopped Bernie Sanders in his tracks in the industrial Midwest by taking Ohio and Illinois.

The Republican Party, meanwhile, veered closer to a contested convention after Kasich held his own state and deprived Trump of its 66 delegates. That makes it more difficult for the billionaire to reach the 1,237 delegates he needs to capture the GOP prize.

Trump did, however, prevail in the biggest contest of the night, taking all of Florida's 99 delegates. That resounding win helped force Rubio out of the race after failing to win his own state and unite the Republican establishment against Trump. The real estate tycoon also won primaries in Illinois and North Carolina.

"This was a great evening," he said. "This was an amazing evening."

The drama is still unfolding in other key races. Trump and Texas Sen. Ted Cruz are locked in a tight battle for Missouri. And Clinton is still hoping for a sweep, with votes still being counted in the close race with Sanders in Missouri.

Vote counting was completed for the night in Missouri with both Clinton and Trump clinging to tight leads of less than half a percentage point, but CNN will not project a winner in either contest as the margin of victory in each case is less than 1 percentage point.

Trump was already looking forward to the general election as he urged party unity amid growing speculation about the potential for a convention fight.

"We have to bring our party together," he said. "We have to bring it together."

Still, GOP leaders may now look to Kasich as their final chance to unite behind a candidate who could challenge Trump in the event of a contested convention.

"We are all very, very happy," Kasich told CNN's Wolf Blitzer in a telephone interview.

According to CNN estimates, Trump needs to win about 60% of the remaining delegates available in the GOP race -- a goal complicated by the fact that some states award delegates on a proportional basis, rather than doling out their entire hauls to the winner, as is the case in Ohio and Florida.

But it's unclear how Kasich, a contender who has won only one state and who has been laboring in obscurity for much of the race, can overtake Trump, who has now won 18 states and is far ahead in the delegate race.

The billionaire, who has harnessed the anger of grass-roots Republicans against party elites, is responsible for destroying the campaigns of some of the GOP's most imposing personalities -- all of whom were once considered strong White House contenders, including Rubio, Jeb Bush and Chris Christie.

Democrats battle it out

On the Democratic side, Clinton has won the Illinois, North Carolina, Florida and Ohio primaries -- crucial victories that bolster Clinton's claim that she is her party's only candidate who can win diverse states that will be pivotal in the November general election.

Her win in North Carolina completed her sweep of Southern states, where she has enjoyed strong support from African-American voters.

"We are moving closer to securing the Democratic Party nomination and winning this election in November," Clinton said in a victory speech in West Palm Beach, Florida.

Clinton said that by the end of the night, she would have two million more votes than Sanders, and hold a lead of more than 300 in the delegate count. While Clinton did not urge Sanders to quit the race so she could turn her fire on Trump, her comments appeared to be a gentle message to her stronger-than-expected challenger.

Photos: Hillary Clinton's life in the spotlight Photos: Hillary Clinton's life in the spotlight Hillary Clinton accepts the Democratic Party's nomination for president at the Democratic National Convention in Philadelphia on July 28, 2016. The former first lady, U.S. senator and secretary of state was the first woman to lead the presidential ticket of a major political party. Hide Caption 1 of 43 Photos: Hillary Clinton's life in the spotlight Before marrying Bill Clinton, she was Hillary Rodham. Here she attends Wellesley College in Massachusetts. Her commencement speech at Wellesley's graduation ceremony in 1969 attracted national attention. After graduating, she attended Yale Law School. Hide Caption 2 of 43 Photos: Hillary Clinton's life in the spotlight Rodham was a lawyer on the House Judiciary Committee, whose work led to impeachment charges against President Richard Nixon in 1974. Hide Caption 3 of 43 Photos: Hillary Clinton's life in the spotlight In 1975, Rodham married Bill Clinton, whom she met at Yale Law School. He became the governor of Arkansas in 1978. In 1980, the couple had a daughter, Chelsea. Hide Caption 4 of 43 Photos: Hillary Clinton's life in the spotlight Arkansas' first lady, now using the name Hillary Rodham Clinton, wears her inaugural ball gown in 1985. Hide Caption 5 of 43 Photos: Hillary Clinton's life in the spotlight The Clintons celebrate Bill's inauguration in Little Rock, Arkansas, in 1991. He was governor from 1983 to 1992, when he was elected President. Hide Caption 6 of 43 Photos: Hillary Clinton's life in the spotlight Bill Clinton comforts his wife on the set of "60 Minutes" after a stage light broke loose from the ceiling and knocked her down in January 1992. Hide Caption 7 of 43 Photos: Hillary Clinton's life in the spotlight In June 1992, Clinton uses a sewing machine designed to eliminate back and wrist strain. She had just given a speech at a convention of the International Ladies' Garment Workers Union. Hide Caption 8 of 43 Photos: Hillary Clinton's life in the spotlight During the 1992 presidential campaign, Clinton jokes with her husband's running mate, Al Gore, and Gore's wife, Tipper, aboard a campaign bus. Hide Caption 9 of 43 Photos: Hillary Clinton's life in the spotlight Clinton accompanies her husband as he takes the oath of office in January 1993. Hide Caption 10 of 43 Photos: Hillary Clinton's life in the spotlight The Clintons share a laugh on Capitol Hill in 1993. Hide Caption 11 of 43 Photos: Hillary Clinton's life in the spotlight Clinton unveils the renovated Blue Room of the White House in 1995. Hide Caption 12 of 43 Photos: Hillary Clinton's life in the spotlight Clinton waves to the media in January 1996 as she arrives for an appearance before a grand jury in Washington. The first lady was subpoenaed to testify as a witness in the investigation of the Whitewater land deal in Arkansas. The Clintons' business investment was investigated, but ultimately they were cleared of any wrongdoing. Hide Caption 13 of 43 Photos: Hillary Clinton's life in the spotlight The Clintons hug as Bill is sworn in for a second term as President. Hide Caption 14 of 43 Photos: Hillary Clinton's life in the spotlight The first lady holds up a Grammy Award, which she won for her audiobook "It Takes a Village" in 1997. Hide Caption 15 of 43 Photos: Hillary Clinton's life in the spotlight The Clintons dance on a beach in the U.S. Virgin Islands in January 1998. Later that month, Bill Clinton was accused of having a sexual relationship with former White House intern Monica Lewinsky. Hide Caption 16 of 43 Photos: Hillary Clinton's life in the spotlight Clinton looks on as her husband discusses the Monica Lewinsky scandal in the Roosevelt Room of the White House on January 26, 1998. Clinton declared, "I did not have sexual relations with that woman." In August of that year, Clinton testified before a grand jury and admitted to having "inappropriate intimate contact" with Lewinsky, but he said it did not constitute sexual relations because they had not had intercourse. He was impeached in December on charges of perjury and obstruction of justice. Hide Caption 17 of 43 Photos: Hillary Clinton's life in the spotlight The first family walks with their dog, Buddy, as they leave the White House for a vacation in August 1998. Hide Caption 18 of 43 Photos: Hillary Clinton's life in the spotlight President Clinton makes a statement at the White House in December 1998, thanking members of Congress who voted against his impeachment. The Senate trial ended with an acquittal in February 1999. Hide Caption 19 of 43 Photos: Hillary Clinton's life in the spotlight Clinton announces in February 2000 that she will seek the U.S. Senate seat in New York. She was elected later that year. Hide Caption 20 of 43 Photos: Hillary Clinton's life in the spotlight Clinton makes her first appearance on the Senate Environment and Natural Resources Committee. Hide Caption 21 of 43 Photos: Hillary Clinton's life in the spotlight Sen. Clinton comforts Maren Sarkarat, a woman who lost her husband in the September 11 terrorist attacks, during a ground-zero memorial in October 2001. Hide Caption 22 of 43 Photos: Hillary Clinton's life in the spotlight Clinton holds up her book "Living History" before a signing in Auburn Hills, Michigan, in 2003. Hide Caption 23 of 43 Photos: Hillary Clinton's life in the spotlight Clinton and another presidential hopeful, U.S. Sen. Barack Obama, applaud at the start of a Democratic debate in 2007. Hide Caption 24 of 43 Photos: Hillary Clinton's life in the spotlight Obama and Clinton talk on the plane on their way to a rally in Unity, New Hampshire, in June 2008. She had recently ended her presidential campaign and endorsed Obama. Hide Caption 25 of 43 Photos: Hillary Clinton's life in the spotlight Obama is flanked by Clinton and Vice President-elect Joe Biden at a news conference in Chicago in December 2008. He had designated Clinton to be his secretary of state. Hide Caption 26 of 43 Photos: Hillary Clinton's life in the spotlight Clinton, as secretary of state, greets Russian Prime Minister Vladimir Putin during a meeting just outside Moscow in March 2010. Hide Caption 27 of 43 Photos: Hillary Clinton's life in the spotlight The Clintons pose on the day of Chelsea's wedding to Marc Mezvinsky in July 2010. Hide Caption 28 of 43 Photos: Hillary Clinton's life in the spotlight In this photo provided by the White House, Obama, Clinton, Biden and other members of the national security team receive an update on the mission against Osama bin Laden in May 2011. Hide Caption 29 of 43 Photos: Hillary Clinton's life in the spotlight Clinton checks her Blackberry inside a military plane after leaving Malta in October 2011. In 2015, The New York Times reported that Clinton exclusively used a personal email account during her time as secretary of state. The account, fed through its own server, raises security and preservation concerns. Clinton later said she used a private domain out of "convenience," but admits in retrospect "it would have been better" to use multiple emails. Hide Caption 30 of 43 Photos: Hillary Clinton's life in the spotlight Clinton arrives for a group photo before a forum with the Gulf Cooperation Council in March 2012. The forum was held in Riyadh, Saudi Arabia. Hide Caption 31 of 43 Photos: Hillary Clinton's life in the spotlight Obama and Clinton bow during the transfer-of-remains ceremony marking the return of four Americans, including U.S. Ambassador Christopher Stevens, who were killed in Benghazi, Libya, in September 2012. Hide Caption 32 of 43 Photos: Hillary Clinton's life in the spotlight Clinton ducks after a woman threw a shoe at her while she was delivering remarks at a recycling trade conference in Las Vegas in 2014. Hide Caption 33 of 43 Photos: Hillary Clinton's life in the spotlight Clinton, now running for President again, performs with Jimmy Fallon during a "Tonight Show" skit in September 2015. Hide Caption 34 of 43 Photos: Hillary Clinton's life in the spotlight Clinton testifies about the Benghazi attack during a House committee meeting in October 2015. "I would imagine I have thought more about what happened than all of you put together," she said during the 11-hour hearing. "I have lost more sleep than all of you put together. I have been wracking my brain about what more could have been done or should have been done." Months earlier, Clinton had acknowledged a "systemic breakdown" as cited by an Accountability Review Board, and she said that her department was taking additional steps to increase security at U.S. diplomatic facilities. Hide Caption 35 of 43 Photos: Hillary Clinton's life in the spotlight U.S. Sen. Bernie Sanders shares a lighthearted moment with Clinton during a Democratic presidential debate in October 2015. It came after Sanders gave his take on the Clinton email scandal. "The American people are sick and tired of hearing about the damn emails," Sanders said. "Enough of the emails. Let's talk about the real issues facing the United States of America." Hide Caption 36 of 43 Photos: Hillary Clinton's life in the spotlight Clinton is reflected in a teleprompter during a campaign rally in Alexandria, Virginia, in October 2015. Hide Caption 37 of 43 Photos: Hillary Clinton's life in the spotlight Clinton walks on her stage with her family after winning the New York primary in April. Hide Caption 38 of 43 Photos: Hillary Clinton's life in the spotlight After Clinton became the Democratic Party's presumptive nominee, this photo was posted to her official Twitter account. "To every little girl who dreams big: Yes, you can be anything you want -- even president," Clinton said. "Tonight is for you." Hide Caption 39 of 43 Photos: Hillary Clinton's life in the spotlight Obama hugs Clinton after he gave a speech at the Democratic National Convention in Philadelphia. The president said Clinton was ready to be commander in chief. "For four years, I had a front-row seat to her intelligence, her judgment and her discipline," he said, referring to her stint as his secretary of state. Hide Caption 40 of 43 Photos: Hillary Clinton's life in the spotlight Clinton arrives at a 9/11 commemoration ceremony in New York on September 11. Clinton, who was diagnosed with pneumonia two days before, left early after feeling ill. A video appeared to show her stumble as Secret Service agents helped her into a van. Hide Caption 41 of 43 Photos: Hillary Clinton's life in the spotlight Clinton addresses a campaign rally in Cleveland on November 6, two days before Election Day. She went on to lose Ohio -- and the election -- to her Republican opponent, Donald Trump. Hide Caption 42 of 43 Photos: Hillary Clinton's life in the spotlight After conceding the presidency to Trump in a phone call earlier, Clinton addresses supporters and campaign workers in New York on Wednesday, November 9. Her defeat marked a stunning end to a campaign that appeared poised to make her the first woman elected US president. Hide Caption 43 of 43

Clinton's victory in Ohio follows her surprise loss in Michigan last week, which raised fresh questions about her campaign strategy and provided a lift to Sanders that he hoped would help him sweep the Midwest. That loss may ultimately turn out to be an anomaly given her wins in Illinois and Ohio.

She unveiled a retooled message in her victory speech that simultaneously rationalized her campaign against Sanders and foreshadowed a general election duel with Trump, as she stressed repeatedly she would create jobs as president and stand up for the middle class.

"We are going to stand up for American workers and make sure no one takes advantage of us -- not China, not Wall Street, not overpaid corporate executives," she said.

Clinton's victories on Tuesday give Sanders a tough climb if he is to grab the nomination.

He would need to win about 72% of the remaining delegates in order to do so, according to CNN estimates, and time may be running out for him unless he can start racking up huge victory margins in coming state contests. Still, most Democratic strategists expect Sanders to stay in the race for several months.

Rubio drops out

With Rubio's decision to drop out, three Republican candidates remain in the White House race -- Trump, Kasich and Cruz.

Photos: Moments from Marco Rubio's career Photos: Moments from Marco Rubio's career Florida Sen. Marco Rubio speaks in October 2013 at the Values Voter Summit, held by the Family Research Council in Washington. Hide Caption 1 of 20 Photos: Moments from Marco Rubio's career Sen. Mike Lee, left, and Rubio talk before a news conference to introduce their proposal for an overhaul of the tax code in March. Hide Caption 2 of 20 Photos: Moments from Marco Rubio's career Rubio, center, arrives in the House chamber ahead of Israeli Prime Minister Benjamin Netanyahu's address to a joint meeting of the U.S. Congress in March. Hide Caption 3 of 20 Photos: Moments from Marco Rubio's career Rubio speaks with the media after delivering remarks during the graduation of small business owners from the Goldman Sachs 10,000 Small Businesses program held in Miami in February. Hide Caption 4 of 20 Photos: Moments from Marco Rubio's career Rubio talks to aides in December before speaking on President Barack Obama's announcement about revising policies on U.S.-Cuba relations. Hide Caption 5 of 20 Photos: Moments from Marco Rubio's career Rubio, left, talks to Sen. Lindsey Graham prior to a news conference on Capitol Hill in July. Hide Caption 6 of 20 Photos: Moments from Marco Rubio's career Rubio talks to reporters in June after a closed door briefing on Capitol Hill. Hide Caption 7 of 20 Photos: Moments from Marco Rubio's career Rubio speaks to the media in front of a wall dedicated to the victims of the violence in Venezuela as he shows support for the Venezuelan community at a restaurant in Doral, Florida, in April 2014. Hide Caption 8 of 20 Photos: Moments from Marco Rubio's career Rubio speaks to the media at the Doral restaurant in April 2014. Hide Caption 9 of 20 Photos: Moments from Marco Rubio's career Rubio checks his phone in March as he arrives for a Capitol Hill news conference to introduce a proposal for an overhaul of the tax code. Hide Caption 10 of 20 Photos: Moments from Marco Rubio's career Rubio, left, is greeted as he arrives at a restaurant in Doral in February 2014. Hide Caption 11 of 20 Photos: Moments from Marco Rubio's career Rubio, left, and Florida Gov. Rick Scott speak to the media in Doral in February 2014. Hide Caption 12 of 20 Photos: Moments from Marco Rubio's career From left, Sens. Cory Booker, Rubio, Kristen Gillibrand and John McCain wait for Obama to deliver the State of the Union address in January 2014. Hide Caption 13 of 20 Photos: Moments from Marco Rubio's career Rubio addresses an event held by the American Enterprise Institute for Public Policy Research in January 2014. Hide Caption 14 of 20 Photos: Moments from Marco Rubio's career Paralympian Brad Snyder poses with Rubio during a Team USA Congressional visit in November 2013. Hide Caption 15 of 20 Photos: Moments from Marco Rubio's career Rubio speaks in November 2013 during a campaign stop for Virginia Attorney General Ken Cuccinelli, the Republican candidate for governor of Virginia. Hide Caption 16 of 20 Photos: Moments from Marco Rubio's career Rubio confers with McCain as U.S. Ambassador to Syria Robert Ford testifies before the Senate Foreign Relations Committee in October 2013. Hide Caption 17 of 20 Photos: Moments from Marco Rubio's career Rubio, center, speaks to members of the media as Sen. Ron Johnson, left, and Rep. Ron DeSantis listen during a news conference on Capitol Hill in October 2013. Hide Caption 18 of 20 Photos: Moments from Marco Rubio's career Rubio returns to the Capitol after meeting with Obama and other Republican leaders about the government shutdown in October 2013. Hide Caption 19 of 20 Photos: Moments from Marco Rubio's career Rubio speaks to an aide on Capitol Hill as he arrives for the weekly Senate Republican Policy Committee luncheon in September 2013. Hide Caption 20 of 20

In a speech that served as a thinly-veiled rebuke of Trump's campaign tactics, Rubio warned that the politics of division will leave America a "fractured nation."

"America is in the middle of a real political storm, a real tsunami and we should have seen this coming," Rubio said. "While we are on the right side," he said, "this year, we will not be on the winning side."

Rubio spent the final weeks of his campaign in an often bitter fight with Trump. But on Tuesday night, Trump congratulated the Florida senator "for having run a tough campaign."

"He is tough," Trump said. "He is smart and he has got a great future."

Cruz also praised Rubio warmly, saying he could "paint a picture and weave a tapestry about the promise of America like nobody else."

And Cruz told Rubio's bereft supporters: "We welcome you with open arms."