Hillary Clinton, who joked about taking the stage wearing “an asbestos pantsuit” Thursday night, won what could turn out to be the critical debate of the race for the Democratic presidential nomination.

To suggest otherwise would be to underestimate the power, the authority and, yes, the intangibly presidential quality of Clinton’s response to a question posed mid-way through the Las Vegas debate by CNN’s Campbell Brown.

Brown asked about a speech the New York senator recently gave at her alma mater, Wellesley College in Massachusetts. Clinton had told the Wellesley crowd, “[In] so many ways, this all women’s college prepared me compete in the all boys’ club of presidential politics.”

“What did you mean at Wellesley when you referred to the boy’s club?” asked Brown.

Clinton paused. She smiled like the Cheshire cat.

“Campbell!” the Democratic frontrunner declared in mock exasperation.

Clinton’s point was made. Everyone got it. Of course, there is a boy’s club — in politics and in media — and that cannot come as news to Campbell Brown.

But the senator, who understood she was finally regaining ground lost after several tough weeks as a frontrunner under assault, was not going to let this magic moment pass quickly.

“It is clear, I think, from women’s experiences, that from time to time, there may be some impediments,” Clinton continued, taking every advantage of the sort of opening that rarely comes in a live and relatively unscripted political setting.

“[It] has been my goal, over the course of my lifetime, to be part of this great movement of progress that includes all of us but has particularly been significant to me as a woman,” said Clinton, who suggested that her campaign seeks to break through “the highest, hardest glass ceiling.”

Clinton had rehearsed this answer. That was beyond debate.

But it worked. She was pulling heartstrings when she spoke of parents driving daughters hundreds of miles to meet the candidate who could be the first woman president and of elderly women who were born when only men had the right to vote tell her that, “I want to live long enough to see a woman in the White House.”

Clinton was playing the gender card — even if she denied doing so.

“I’m not playing, as some people say, the gender card here in Las Vegas, I’m just trying to play the winning card,” the candidate chirped. “I understand very well that people are not attacking me because I’m a woman. They’re attacking me because I’m ahead.”

The senator was having it both ways. Even as she cashed in on the fact that she is mounting a historic campaign for the presidency — not the first by a woman, but the first in which a woman might prevail — Clinton said she was not “running because I’m a woman.” Rather, she said, “I’m running because I think I’m the best qualified and experienced person to hit the ground running.”

Clinton left her most aggressive challengers, both of whom had been gaining ground on her going into Thursday night’s debate, no space.

When former North Carolina Senator John Edwards followed Clinton’s “not-playing-the-gender-card” soliloquy with a mild criticism of the frontrunner, he was roundly booed by the crowd.

Not long afterward, when Illinois Senator Barack Obama took a swing at Clinton, he was booed just as loudly.

Clinton had cornered them. They had no room for movement.

She won the night, and she might well have won a great deal more.