Hillary Clinton, whose convention in 2016 featured the special effect of her image smashing a virtual glass ceiling, made the case for electing the first woman president, an angle that Ms. Harris has resisted emphasizing. Mrs. Clinton placed Ms. Harris in a line of political women that included Shirley Chisholm and the suffragists. (She referenced the dramatic passage of the 19th Amendment, a scene dramatized in the musical “Suffs,” which she produced.) She also wryly drew a parallel to herself. Mr. Trump, she said of Ms. Harris, was “mocking her name and her laugh. Sounds familiar.”

But the most challenging piece of political staging came last: having President Biden give a valediction and an endorsement of his vice president in a race that he had been pressured to leave. The night’s climax had to convey both celebration of Mr. Biden’s first term and excitement at the fact that he wasn’t seeking a second; it needed to be the kind of sad that leaves you with a smile on your face, not a pit in your stomach.

Mr. Biden took the stage after a warm introduction by his daughter Ashley Biden, pulling out a handkerchief to dab away a tear. His address was in the shouty, fierce style of his more effective recent speeches, a marked contrast to the happy-warrior style that Ms. Harris has already made her campaign’s hallmark. But there were moments of emotion too, as he faced the sudden end of a long career: “America, I gave my best to you.”

In the room, at least, the speech seemed to go over, if not without some dissonance. Nancy Pelosi, a key figure in pressuring Mr. Biden to leave the race, was on camera hoisting a “We [Heart] Joe” sign. Meanwhile, Fox News commentators became Mr. Biden’s most ardent sympathizers. “Poor Joe unfortunately was kicked to the curb in a political coup,” said Sean Hannity.

Cramming together past and future, anticipation and commemoration, takes a lot of time, however. The program, stuffed with speakers and behind schedule, ran so late that Mr. Biden didn’t take the stage until well after prime-time in the Eastern time zone. Not that he seemed in a rush to leave.

But with Ms. Harris embracing him at the end of his farewell, the cast change was complete. She has three more nights to make the show her own.