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 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 strongly defended 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.”