The tone firmly set, she continued: “Democrats are not going to win if we have a nominee who has a history of hiding his tax returns, of harassing women, and of supporting racist policies like redlining and stop-and-frisk. Look, I’ll support whoever the Democratic nominee is. But understand this: Democrats take a huge risk if we just substitute one arrogant billionaire for another.”

She went on to criticize the health care plans released by Mr. Buttigieg (“It’s not a plan; it’s a PowerPoint”), Ms. Klobuchar (“It’s like a Post-it note: ‘Insert plan here’”), and Mr. Sanders (“a good start, but instead of expanding and bringing in more people to help, instead his campaign relentlessly attacks everyone who asks a question or tries to fill in details”).

And then she turned back to Mr. Bloomberg in one of the most memorable moments of the night.

The subject was the nondisclosure agreements that employees of Mr. Bloomberg’s company signed following allegations of harassment and discrimination based on gender. Mr. Bloomberg, in response, had pointed to his hiring and promotion of women, and to descriptions of his company as a good place to work.

“I hope you heard what his defense was: ‘I’ve been nice to some women,’” Ms. Warren replied. Mr. Bloomberg rolled his eyes.

As the exchange went on, it began to sound rather like a prosecution.

WARREN: What we need to know is exactly what’s lurking out there. He has gotten some number of women — dozens, who knows — to sign nondisclosure agreements both for sexual harassment and for gender discrimination in the workplace. So, Mr. Mayor, are you willing to release all of those women from those nondisclosure agreements so we can hear their side of the story? BLOOMBERG: We have a very few nondisclosure agreements. WARREN: How many is that? BLOOMBERG: Let me finish. WARREN: How many is that? BLOOMBERG: None of them accuse me of doing anything other than maybe they didn’t like a joke I told. These are agreements between two parties that wanted to keep it quiet, and that’s up to them. They signed those agreements, and we’ll live with it. WARREN: So wait, when you say it is up to them, I just want to be clear: ‘some’ is how many? And when you say they signed them and they wanted them, if they wish now to speak out and tell their side of the story about what it is they allege, that’s now OK with you? You’re releasing them on television tonight? Is that right? BLOOMBERG: Senator, no. Senator, the company and somebody else in this case — the man or woman, or could be more than — they decided when they made an agreement, they wanted to keep it quiet for everybody’s interests. They signed the agreements, and that’s what we’re going to live with. WARREN: I’m sorry, no, the question is: Are the women bound by being muzzled by you? And you could release them from that immediately. Because understand, this is not just a question of the mayor’s character. This is also a question about electability. We are not going to beat Donald Trump with a man who has who knows how many nondisclosure agreements and the drip, drip, drip of stories of women saying they have been harassed and discriminated against.

Even before the debate had ended, some commentators — including the conservative Washington Post columnist Jennifer Rubin and the actor Ken Olin — were criticizing Ms. Warren as “mean,” “angry” and “nasty.”

But others saw it quite differently.

“I’ve never seen anything like that on a presidential stage from a woman — it was mind-blowing,” Rebecca Traister, a writer for New York magazine and the author of “Good and Mad: The Revolutionary Power of Women’s Anger,” said in an interview afterward. “Look, I found it exhilarating and historic, but there’s no question that it’s a risk.”

It is hard, Ms. Traister said, to predict the long-term impact of something that hasn’t happened before.