In her debate on Wednesday with Donald J. Trump, Hillary Clinton for the first time emerged as the clarion-voiced advocate for women whom many liberal women had been longing for — especially the younger voters she had largely left cold throughout the Democratic primaries.
Speaking ardently on abortion rights, a defining issue for an older generation of feminists, Mrs. Clinton dispensed with Democrats’ longstanding caveat that the procedure should be rare, and gave a fierce defense of women’s right to control their own bodies without government interference.
More tellingly, Mrs. Clinton also seemed to speak to a new generation of women — and to many young men — by assailing Mr. Trump over sexual assault and harassment, saying his dismissals of the allegations against him by multiple women showed that he “thinks belittling women makes him bigger.”
“He goes after their dignity, their self-worth,” Mrs. Clinton said firmly. “And I don’t think there is a woman anywhere who doesn’t know what that feels like.”
Perhaps the biggest boost she received, however, was one that neither she nor any army of political operatives could have engineered: when Mr. Trump interjected, “What a nasty woman,” as Mrs. Clinton was discussing Social Security and taxes.
Overnight, his insult became a battle cry for Mrs. Clinton’s partisans — including many whose passions she had not yet stirred. “Nasty Woman” T-shirts began selling on the internet. Naral Pro-Choice America advertised “NastyWoman” stickers. A New York City man quickly set up an expletive-laced “nasty women” website that redirected visitors to Mrs. Clinton’s campaign page. Streams of Janet Jackson’s 1986 hit “Nasty” increased 250 percent on Spotify after the debate, according to a Spotify spokesman. More than 8,000 people had taken up the phrase on Twitter by midafternoon, wielding it as a badge of honor.
A campaign that a day earlier had taken some ribbing over a leaked email showing that top aides churned through a list of more than 80 potential slogans — many of them plodding and colorless — suddenly seemed to be taking on the vitality of a grass-roots movement.
Even before Wednesday night’s debate, Mrs. Clinton had been beating Mr. Trump by large margins among probable female voters. Sixty percent supported Mrs. Clinton, compared with 24 percent who supported Mr. Trump, according to a CBS poll conducted in October, just days after the release of a tape in which Mr. Trump could be heard boasting about his ability to get away with sexual assault.
But many women seemed motivated as much, or more, by fear of a Trump presidency as by enthusiasm for Mrs. Clinton.
“Donald Trump’s candidacy has just terrified me from the moment he stepped on the stage,” said April Alario, 35, a disabled former pastor in Boston.
“He reminded me of every controlling abusive man I’ve ever encountered,” added Ms. Alario, who said she had voted Republican in every presidential election since 2004.
On Wednesday night, however, Mrs. Clinton powerfully made her case to younger women on subjects that polls show matter most to them: sexual harassment, marriage equality and women’s rights.
Amanda Silberling, a junior at the University of Pennsylvania who is a campus advocate against sexual assault, watched the debate with a group of students while making T-shirts that mock Mr. Trump over the sexual-assault and harassment allegations against him.
Ms. Silberling said she favored Bernie Sanders in the Democratic primary campaign, but that she went from merely opposing Mr. Trump to avidly supporting Mrs. Clinton during the debate, as Mrs. Clinton repeatedly took him to task on the issues of sexual assault and abortion rights, including for late-term procedures.
“For women, politics gets complicated when people try to place ownership on what a woman can and can’t do with her body,” she said. “It does reassure me to have a woman in office who understands what it’s like to be a woman.”
To older Democratic women, who never took the right to abortion for granted — and for whom preservation of the 1973 decision in Roe v. Wade is a touchstone — Mrs. Clinton won a new round of approval Wednesday with her staunch defense of even the late-term procedure denounced by its critics as partial-birth abortion.
Not only did she rebuff Mr. Trump’s contention that such abortions “rip the baby out of the womb of the mother just prior to the birth,” but Mrs. Clinton upbraided him for using what she called “scare rhetoric.”
Then she availed herself of an argument with conservative roots: “I’ve been to countries where governments either forced women to have abortions, like they used to do in China, or forced women to bear children, like they used to do in Romania,” she said.
“And I can tell you,” she said, “the government has no business in the decisions that women make with their families, in accordance with their faith, with medical advice.”
Of course, abortion rights is not exclusively a concern for women born before 1980.
Chelsea Donaldson, 27, a law school student in Springfield, Mass., who voted for Bernie Sanders in the primary, posted on Twitter a “thank you” to Mrs. Clinton for her remarks on abortion during the debate.
Ms. Donaldson said later that she refused to “go back to the time period of my grandmothers” when abortion was illegal.
“I was thrilled to see that she not only supported the right to access, but shot down Trump’s ludicrous comments about late-term abortion,” Ms. Donaldson said by email. She said she felt “energized” at how Mrs. Clinton explained the stakes.
Still, Mrs. Clinton has struggled to connect with younger voters, who polls show place less of a priority on reproductive rights as an issue — either because they feel morally conflicted about it or because they take reproductive rights for granted.
A 2013 study by the Pew Research Center showed that 62 percent of Americans ages 18 to 29 said abortion was “not that important” compared with other issues.
Only 44 percent of Americans under 30 knew what Roe v. Wade was about.
By contrast, marriage equality — a civil rights fight that younger voters lived through, and that many participated in — resonates much more.
Among millennials, 81 percent of Americans aged 18 to 29 said that same-sex couples should be allowed to marry, according to the CBS poll.
And Mrs. Clinton made sure to mention the importance of preserving marriage equality, alongside abortion rights, when she was asked about the criteria she would use to pick judges for the Supreme Court.
That meant a lot to Rebecca Bean, 31, of Wisconsin Dells, Wis., whose brother, an Iraq War veteran, is married to a man.
“Knowing that they are not going to lose their rights is important,” she said.
But Ms. Bean, who initially supported Mr. Sanders for president, also has another reason to support Mrs. Clinton in this race.
The sexual allegations against Mr. Trump have affected her in a personal way, as she made clear in a Twitter post on Thursday.
“IamANastyWomanBecause I am a survivor of sexual assault,” she wrote, “who helps others in unsafe and unhealthy relationships.”