I know what you’re thinking. So let’s just get it out of the way: Like buttah. Like satin. Like whatever that perfume is that Elizabeth Taylor hawked. Oh, right: White Diamonds. Barbra Streisand sounded like diamonds. And porcelain and a freshly drawn bath and consommé.

The voice is 74. So maybe the carats are fewer, but so what? It remains The Voice. Thursday night at Barclays Center in Brooklyn, it never asked to be received in pity, graded on a curve or helped across the street. There was some nervousness beforehand that it would be somehow … off.

But no: On, on, on. For example, its owner continues to make the finale of “Don’t Rain on My Parade” sound like a space shuttle leaving Earth, the gravitational force enough to yank what looked like a sold-out crowd to its feet.

That came well into the second act during a “Funny Girl”-“Funny Lady” stretch, in which Ms. Streisand walked us through the films’ plots, while movie clips played on screen behind her. We didn’t need any of that, but it made a kind of sense. This wasn’t a star doing battle with a former self. It was a woman having fun with the past.

Backed by an elastic band and aided by teleprompters, she spent a lot of her more than two hours onstage explaining the stories behind songs and performances and album covers. Her “A Star Is Born” soundtrack — the third-biggest movie of 1976, by the way — has that great image of a shirtless Kris Kristofferson palming the head of a shirtless Ms. Streisand, their mouths almost meeting, their hunger mutual. Staring up at that cover, she said, “If you’re wondering what I was wearing during this shoot, it was musk.”

For well north of two hours, Ms. Streisand was like that: amusing, self-amused, at home. Before her encore, she chided us for keeping us from her dinner: “My pizza’s getting cold!” People would shout compliments or requests, and she’d talk back. Early on, after “Everything,” from “A Star Is Born,” she said, “There’s just one more thing I want” — which turned into an endorsement for Hillary Clinton’s presidential candidacy. Before doing “Pure Imagination,” Gene Wilder’s song from “Willy Wonka and the Chocolate Factory,” she offered environmental entreaties that made you think she was going to do “Mercy Mercy Me” instead. When it was over, she said, “And that’s why we shouldn’t vote for someone who believes climate change is a hoax,” referring, presumably, to Mrs. Clinton’s opponent, Donald J. Trump.

So the arena became Ms. Streisand’s living room, her audience became guests, and stage patter sometimes took cozy TED Talk turns. Meanwhile, the people in the front rows leapt up so often it was fair to ask whether she was delivering a State of the Union speech too. Ms. Streisand sang about two dozen songs — the ones you’d expect (“People,” “Evergreen,” lots of Stephen Sondheim) and a few, like “Pure Imagination,” which you wouldn’t. That one is on her new duets record, “Encore,” which comes out later this month and has her singing with stars from Melissa McCarthy and Anne Hathaway to Antonio Banderas and Chris Pine. (Her partner on “Pure Imagination” is Seth MacFarlane.)

Ms. Streisand introduced a little highlight reel from those recording sessions and eventually unveiled the actor Patrick Wilson to accompany her on “Loving You” from Mr. Sondheim’s “Passion,” a number that required some acting from Mr. Wilson. He had to play both an ambivalent lover and a man who made perfect sense belting opposite Ms. Streisand. Mission accomplished. Whatever awe he had, he kept tucked away along with the tie he didn’t wear with his black suit.

Jamie Foxx arrived a few songs later, all awe. The crowd went cuckoo for him, and he went cuckoo for her, partly while impersonating Quincy Jones paying Ms. Streisand’s derrière a hilarious compliment. They sang “Climb Ev’ry Mountain” in a way that was more muscular than beautiful, their clasped hands making a better connection than their voices. The climb has rarely sounded so literal. But when they got to the top, the audience got up to cheer for them.

So what was this show? I mean, besides a pleasure to behold. Officially, it’s part of a nine-city tour with a mouthful of a title, “Barbra: The Music… the Mem’ries… the Magic!,” that salutes six decades of albums. (“Encore” is her 35th studio record.) So in many ways this is a celebration of endurance, as opposed to a night of camp or even campiness. You need an “I’m Still Here” or “Have I Stayed Too Long at the Fair” for that, songs that would have been the equivalent of that thing Hulk Hogan would do where he’d put his hand to his ear so we would cheer louder to amplify his triumph. Have I stayed too long? No, Barbra. Absolutely not! She really is too dignified to beg.

As it was, she included “No More Tears (Enough Is Enough),” the torch song she sang with Donna Summer, which costume-changes into a disco anthem. That came last in a medley that included “Stoney End” and “Woman in Love,” and Ms. Streisand mostly vamped while her three very good backup vocalists did their thing at her side.

Ms. Streisand has had a career like nobody else’s. She remains this emblem of volition and charisma and power — the movie star who sings, the singer who acts, the female director who was made to suffer for daring to do what men had always done. She could have spent the night doing nothing but self-consecrating, and no one would have minded. But it’s funny: You don’t go to a Streisand show purely for nostalgia, purely for “The Way We Were,” as much as to witness a great performer in her current formidable state. Nostalgia has always been built into her catalog. But can she make the distant past vital again? She tried to connect before to now. Her antidote to Mr. Trump, for instance, was “People.” Which is to say that it’s not an artistically ambitious show. Its star, alas, is set in her ways. But those ways are what some people expect to see.

We are at a new place with superstardom and age, though. Certain women of the pre-music-video era can now seemingly go on forever. Their fame, in part, resides with an instrument that’s been kept in astounding shape. Some of the nation is still recovering from Aretha Franklin’s shedding a fur coat and bringing down the house in January at the Kennedy Center Honors. She and Ms. Streisand were born a month apart, and this sort of sustained virtuosity feels special among singers of their stature. Neither is the master of phrasing she once was. But what they now lack in contour (Ms. Streisand has even acquired a touch of Ms. Franklin’s rasp), they make up for in dynamism. These two very different women are still giving everything they’ve got. And that’s enough.

We came to Barclays to hear amazement as opposed to see a spectacle. Although the sight of Ms. Streisand singing “Papa, Can You Hear Me” from “Yentl” while appearing to catch the holy spirit, before the end of the first act, was quite something. The power she summoned pimpled the skin and dampened the eyes. I don’t know if Papa could hear this woman, but certainly heaven could.