Hillary Rodham Clinton, seeking to halt the momentum of her insurgent challenger, Senator Bernie Sanders of Vermont, aggressively questioned his values, positions and voting history Tuesday night in the first Democratic presidential debate, turning a showdown that had been expected to scrutinize her character into a forceful critique of his record.

In a series of sometimes biting exchanges, Mrs. Clinton declared that Mr. Sanders was mistaken in his handling of crucial votes on gun control and misguided in his grasp of the essentialness of capitalism to the American identity. Mocking Mr. Sanders’s admiration for the health care system of Denmark, she interrupted a moderator to offer a stinging assessment of his logic, suggesting he was unprepared to grapple with the realities of governing a superpower.

“We are not Denmark,” Mrs. Clinton said, adding with a sly smile, “I love Denmark. We are the United States of America.”

The crowd erupted in applause.

A few moments later, Mrs. Clinton took aim at what may be Mr. Sanders’s greatest vulnerability with the Democratic left, asking why he had voted to shield gun makers and dealers from liability lawsuits. Mr. Sanders, who linked his record on gun control to his representation of a rural state, called the bill “large and complicated.”

“I was in the Senate at the same time,” Mrs. Clinton replied. “It wasn’t that complicated to me. It was pretty straightforward.”

Asked if Mr. Sanders had been tough enough on guns during his decades-long career in Congress, Mrs. Clinton offered a sharp reply: “No. Not at all.”

“I think that we have to look at the fact that we lose 90 people a day from gun violence,” she said. “This has gone on too long, and it’s time the entire country stood up against the N.R.A.”

It was a dominant performance that showcased Mrs. Clinton’s political arsenal: a long record of appearances in presidential debates, intense and diligent preparation, and a nimbleness and humor largely lacking in her male counterparts. She let no opportunity pass her by. When Mr. Sanders described the conflict in Syria as “a quagmire within a quagmire” but said he did not support sending American ground troops there, Mrs. Clinton interjected energetically: “Nobody does. Nobody does, Senator Sanders.”

For Mr. Sanders, the gathering in Las Vegas provided an evening of unexpectedly forceful challenges, both from Mrs. Clinton and from the moderator, Anderson Cooper of CNN. At times, he seemed somewhat exasperated and unsure about how to match Mrs. Clinton’s agility. Perhaps his most memorable moment occurred when he zestfully defended Mrs. Clinton from criticism of her email practices.

“Let me say something that may not be great politics,” he said. “But I think the secretary is right, and that is that the American people are sick and tired of hearing about your damn emails.”

Mrs. Clinton flashed a wide smile and shook her rival’s hand. “Thank you, Bernie,” she said, setting off huge applause in the auditorium.

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Mr. Sanders regained his footing when the debate turned to one of his signature issues: Wall Street and its excesses.

Mrs. Clinton said that her plan to crack down on wrongdoers on Wall Street “would have the potential of actually sending the executives to jail,” but that Mr. Sanders’s proposal to break up banks was naïve. Mr. Sanders grew animated.

“Congress does not regulate Wall Street,” he said, setting off roars from the crowd. “Wall Street regulates Congress.”

He suggested that the real naïveté was Mrs. Clinton’s notion that reaching out to Wall Street was part of the solution. “ ‘Please do the right thing,’ ” he said, “is kind of naïve.”

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And there were reminders of the tendencies that have made the left wing of the Democratic party suspicious of Mrs. Clinton. Prodded about her history of changing positions on major issues, she inelegantly explained why it took her so long to come out against the proposed Canadian American oil pipeline that so many of her rivals already oppose. “I never took a position on Keystone until I took a position on Keystone.”

Mrs. Clinton benefited for much of the night from the tentativeness of her rivals, who appeared wary of directly attacking the figure who represents their party’s best chance at electing a woman president. Instead, they offered oblique criticisms and diplomatic dismissals. In his opening statement, Lincoln Chafee, the former senator and governor of Rhode Island, told the audience: “What I’m most proud of is that, in 30 years of public service, I have had no scandals. I have high ethical standards.”

Jim Webb, the former senator from Virginia, seemed to take a swipe at Mrs. Clinton’s decades in public life and her closeness to Democratic Party insiders, saying the country was looking for somebody “who understands how the system works, who has not been co-opted by it.”

There were exceptions, of course. Former Gov. Martin O’Malley of Maryland, when asked whether Mrs. Clinton would be too quick to use American military force, scolded her for her 2002 Senate vote to authorize military action in Iraq, saying the vote had been carried out “under false pretenses” and calling the war “one of the worst blunders in modern American history.”

Mr. O’Malley, who has struggled to match Mrs. Clinton’s organizational might and Mr. Sanders’s message, repeatedly found ways to stand out, calling for expanding the Affordable Care Act to cover the children of undocumented immigrants.

“We are a nation of immigrants,” he said. “I am for a generous, compassionate America that says we are all in this together.”

As the debate went on, Mr. O’Malley, the youngest of the five candidates at 52, said he had heard from Americans of all stripes that they hungered for new, post-Clinton leadership.

“I respect what Secretary Clinton and her husband have done for our country, but our country needs new leadership to move forward,” he said.

For Mrs. Clinton, the forum was a highly anticipated return to the debate stage after a seven-year hiatus and a season of remarkable political convulsions: the revelation that she relied exclusively on a private email server as secretary of state; the emergence of Mr. Sanders, a once-obscure senator from Vermont, as a potent rival in Iowa and New Hampshire; the threat of Vice President Joseph R. Biden Jr.’s entering the race; and the restless liberal tide within the Democratic electorate that she is struggling to command.

Her assertiveness was striking, given that on the campaign trail, she has seemed unsure of how to neutralize Mr. Sanders’s crowd-luring popularity. Her campaign has feared that attacking a candidate beloved by supporters for his quirky style, raw frustration and unvarnished liberalism could alienate precisely the segment of the Democratic electorate she would need to win the general election.

She seemed highly attuned to what may be her biggest vulnerabilities in 2016: her authenticity and questions about whether she cares about the problems of ordinary people. In a CBS News poll released Sunday, 61 percent of registered voters said they did not trust her, and 48 percent said she did not care about people like them.

In Las Vegas, she smiled and laughed regularly. After a commercial, she joked about the duration of her allotted bathroom break. “It does take me a little longer,” she said.

The debate captured what has emerged as a consensus in the Democratic Party: that urgent action is needed to address the subject of income inequality. Mr. Sanders assailed the power of the nation’s wealthiest and called for Americans to “take back our government from a handful of billionaires.”

But in an incongruous touch, the debate was held at the Wynn hotel, a slender golden curve of Las Vegas excess, conceived by the billionaire Steve Wynn. In a strange tableau for a political party preoccupied with income inequality, a mix of around 1,300 prominent officials and wealthy donors filed into a ballroom down the hall from rows of luxury fashion stores and poker tables. (Before the debate started, one Clinton donor bragged of winning $25,000 at the tables.)

The debate, hosted by CNN, was billed as a prizefight with a network of promotion showing silhouettes of Mr. Sanders and Mrs. Clinton on giant screens overlooking the city’s famed Strip. But it was thick with foreign and domestic policy concerns, rather than the personal insults and colorful exchanges that have characterized the Republican forums.

Yet there were lighter moments. Toward the close of the evening, Mr. Cooper asked the candidates whom they were most proud to call an enemy. The contenders ticked off a list of predictable villains to the left: the coal industry, the National Rifle Association, drug companies and health insurers.

Mrs. Clinton added mischievously: “Iranians, probably the Republicans.”

But it was Mr. Webb, a former marine who fought in Vietnam, who offered an unforgettable answer.

“I’d have to say the enemy soldier that threw the grenade that wounded me, but he’s not around right now to talk to,” he said.

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