(CNN) As Pete Buttigieg has ascended in the polls in the kickoff state of Iowa, it was inevitable that he would eventually become the chief target of the other top Democratic candidates for president.

That finally happened on the debate stage Thursday night, and the South Bend, Indiana, mayor was ready for it.

After a fairly staid first half of the PBS-Politico debate in Los Angeles, Massachusetts Sen. Elizabeth Warren and Vermont Sen. Bernie Sanders seized their moment to fault Buttigieg (as well as former Vice President Joe Biden) for courting the big money donors and bundlers who they themselves have eschewed. Their critiques seemed to open the door for Sen. Amy Klobuchar of Minnesota, who sought to highlight Buttigieg's relative lack of political experience compared with other candidates onstage.

As expected, the rhetoric got the most heated when Warren cited a recent fundraiser that Buttigieg held in a "wine cave" beneath a chandelier adorned with some 1,500 Swarovski crystals. For more than a week, both the Sanders and Warren campaigns seized on that event as an example of how big money can corrupt politics, compared with their own pursuits of small-dollar grassroots donations.

Warren, who has dipped in the polls and is competing heavily with Buttigieg for white-college educated voters, began with an implicit nudge at Buttigieg by noting that she offers pictures in her famed "selfie" line for free, comparing that tactic to candidates who ask donors for financial contributions in exchange for pictures.

"I can't help but feel that might have been directed at me," Buttigieg said, raising his hand to respond. He argued that Democrats are in "the fight of our lives " against President Donald Trump, who has already amassed $300 million for the campaign despite being impeached this week.

"This is our only chance to defeat Donald Trump. And we shouldn't try to do it with one hand tied behind our back," Buttigieg said, noting that he welcomes contributions from $10 all the way up to the limit. But Warren pounced.

"The mayor just recently had a fundraiser that was held in a wine cave full of crystals and served $900-a-bottle wine. Think about who comes to that," Warren said. "... I do not sell access to my time. I don't spend time with millionaires and billionaires. I don't meet behind closed doors."

Buttigieg suggested that she was being hypocritical since she has courted high-dollar donors in past campaigns, and noted that according to Forbes magazine, "I'm literally the only person on this stage who is not a millionaire or billionaire."

"This is the problem with issuing purity tests you cannot yourself pass," the South Bend mayor said to Warren.

Sanders interjected that Biden has received contributions from 44 billionaires, compared with the 39 billionaires who have contributed to Buttigieg.

"So, Pete, we look forward to you -- I know you are an energetic guy and a competitive guy -- to see if you can take on Joe on that issue," Sanders said pointedly, as the crowd acknowledged the sharpness of the dig. "But what is not -- what is not a laughing matter, my friends: This is why three people own more wealth than the bottom half."

Biden defended himself by noting the average contribution to his campaign is $43.

"The idea that the senator suggested, that I am in the pocket of billionaires when, in fact, they oppose everything that I have ever done and continue to do," Biden said.

Businessman Andrew Yang, who offered moments of levity and humor throughout the night, tried to steer the conversation back to the original question, which had been about former President Barack Obama's remark that many of the world's problems could be solved if more women were in power -- and part of the problem is that older, white men don't get out of the way.

"Money and men are tied together," Yang said after the Warren-Buttigieg contretemps. "The fact is strong societies would elect more female leaders. ... I'm on the record saying that you need both strong men and female leaders in government because the fact is if you get too many men alone and leave us alone for a while, we kind of become morons."

Pushing for his plan to give $100 a year to every American adult to donate to political campaigns, Yang added that more Americans would contribute to campaigns, leading to more diversity in leadership.

"You would have many, many more women that would run for office because they don't have to shake the money tree in the wine cave," Yang said.

Once the sparring began, it seemed hard for the top candidates to hold back.

Klobuchar chided Buttigieg for, in her view, minimizing the experience of the current and former senators on the stage by noting that he is not a part of the culture of Washington.

"When we were in the last debate, Mayor, you basically mocked the 100 years of experience on the stage," Klobuchar said. "I see Elizabeth (Warren), who started the Consumer Protection Financial Bureau and helping 29 million people. I see the vice president's work in getting $2 billion for his cancer (initiative). I see Sen. Sanders working to get the veterans bill passed across the aisle, and I see what I have done, which is to negotiate three farm bills and be someone that actually had major provisions put in those bills."

"So while you can dismiss committee hearings, I think this experience works. And I have not denigrated your experience as a local official."

Buttigieg replied that Klobuchar had, in fact, denigrated his experience, and he noted that he had served in the military. He served as a lieutenant in the Navy Reserve and fought in Afghanistan.

"Let me tell you about my relationship to the First Amendment. It is part of the Constitution that I raised my right hand and swore to defend with my life. That is my experience, and it may not be the same as yours, but it counts, Senator. It counts," he said.

When Klobuchar argued that she was talking about his experience outside the military -- comparing her winning record in the Midwest with his losses in races for chairman of the Democratic National Committee and for Indiana state treasurer -- he was ready with an answer.

"I certainly respect your military experience. That's not what this is about," Klobuchar said. "We should have someone heading up this ticket that has actually won."

"Senator, I know that if you just go by vote totals, maybe what goes on in my city seems small to you," Buttigieg replied. "If you want to talk about the capacity to win, try putting together a coalition to bring you back to office with 80% of the vote as a gay dude in Mike Pence's Indiana."

Candidates tackle race

Standing on a stage that was the least diverse and most male-dominated of the entire campaign, the candidates engaged in a heated discussion over how to make the leadership of their party more reflective of the diversity of the country.

Noting that Democrats rely on black, Hispanic and Asian voters, the PBS-Politico moderators addressed that question to Yang as the only candidate of color on the stage and he was armed with statistics.

"It's both an honor and disappointment to be the lone candidate of color on the stage tonight. I miss Kamala, I miss Cory, although I think Cory will be back," Yang quipped, noting the exit of California Sen. Kamala Harris from the race and that New Jersey Sen. Cory Booker did not meet the criteria for the debate.

"I grew up the son of immigrants and I had many racial epithets used against me as a kid," Yang said. "But black(s) and Latinos have something much more powerful working against them than words. They have numbers. The average net worth of a black household is only 10% that of a white household. For Latinos, it's 12%. A black woman is 320% more likely to die from complications in childbirth. These are the numbers that define race in our country."

He said the problem could be fixed if the government districuted money to Americans to donate to campaigns.

Sanders pointed out that Americans of color will suffer the most "if we do not deal with climate change," arguing that "we have an obligation up here, if there are not any of our African American brothers and sisters up here, to speak about an economy in which African Americans are exploited, where black women die three times at higher rates than white women, where we have a criminal justice system which is racist and broken, disproportionately made up of African Americans, Latinos and Native Americans who are in jail."

Asked how she would talk to Americans who are uncomfortable with the fact that the United States will be majority nonwhite within a generation, Klobuchar was blunt: "I say this is America. You're looking at it," Klobuchar said.

The Minnesota senator said that Democrats must aggressively target voter suppression and gerrymandering, and pass her bill that would register every child in America to vote when they turn 18. Arguing for an agenda of "economic opportunity," Klobuchard added, "because as Martin Luther King Jr. said, what good is it to integrate a lunch counter if you can't afford a hamburger?"

Candidates mostly agree on impeachment

The candidates touched off their discussion by debating who among them could make the most persuasive case that Trump should be removed from office at a time when the public is divided on impeachment.

Sanders called the President a "pathological liar" who is "running the most corrupt administration in the modern history of this country."

He said he would be making the case in the coming weeks "that we have a President who has sold out the working families of this country, who wants to cut Social Security, Medicare and Medicaid after he promised he would not do that."

The only candidate to make a counterargument was Yang, who argued his party should stop obsessing over impeachment and place a greater focus on the problems facing Americans.

"The more we act like Donald Trump is the cause of all our problems, the more Americans lose trust that we can actually see what's going on in our communities and solve those problems," Yang said. "What we have to do is we have to stop being obsessed over impeachment -- which unfortunately strikes many Americans like a ballgame where you know what the score is going to be -- and start actually digging in and solving the problems that got Donald Trump elected in the first place."

Yang added that leaders "have to take every opportunity to present a new, positive vision for the country, a new way forward to help beat him in 2020, because make no mistake, he'll be there at the ballot box for us to defeat."