“This song’s for Manhattan!” Mick Jagger told the crowd on Thursday night at MetLife Stadium, before launching into a punchy rendition of “Shattered,” that agitated ode to late-70s New York City that closes out the band’s 1978 album “Some Girls.” In the ensuing 46 years, the city has changed in some superficial ways but somehow remained essentially the same — much, as they showed throughout an impressively energetic two-hour set, like the Rolling Stones.

The Stones’ first New York-area stadium gig in five years was sponsored, without a hint of irony, by AARP. It was appropriate: At times what transpired onstage felt not just like a rock concert but a display of the evolutionary marvel that is aging in the 21st century. (Albeit aging while wealthy, with every possible technological and medical advantage at one’s disposal. I’ll have whatever vitamins the Stones are taking, please.)

Ronnie Wood, the core group’s baby at age 76, still shreds on the guitar with a grinning, impish verve. Eighty-year-old and eternally cool Keith Richards pairs his bluesy licks with a humble demeanor that seems to say “I can’t believe I’m still here, either.” And then there is Jagger, who turns 81 a few days after the Hackney Diamonds Tour wraps in July. Six decades into his performing career, he is somehow still the indefatigable dynamo he always was, slithering vertically like a charmed snake, chopping the air as if he’s in a kung fu battle against a swarm of unseen mosquitoes, and, when he needs both hands to dance, which is often, nestling the microphone provocatively above the fly of his pants. Sprinting the length of the stage during a rousing “Honky Tonk Women” — the 13th song in the set! — he conjured no other rock star so much as Benjamin Button, as he seemed to become even more energetic as the night went on.

Last year’s “Hackney Diamonds” — the Stones’ first album of new material in nearly two decades — was the nominal reason for the tour, but they didn’t linger on it, and the crowd didn’t seem to mind. Across 19 songs, they played only three tunes from the latest release, including two of the best: The taut, growly lead single “Angry” and, for the first part of the encore, the gospel-influenced reverie “Sweet Sounds of Heaven.” Mostly it was a kind of truncated greatest hits collection, capturing the band’s long transformation from reverent students of the blues (Richards’ star turn on the tender “You Got the Silver”) to countercultural soothsayers (a singalong-friendly “Sympathy for the Devil”) to corporate rock behemoth (they opened, of course, with “Start Me Up”).

Jagger, Richards and Wood all still emanate a palpable joy for what they are doing onstage. But those joys also feel noticeably personal and siloed, rarely blending to provide much intra-band chemistry. That is likely a preservation strategy — the surest way to keep a well-oiled machine running and to continue sharing the stage with the same people for half a century or more. But when Jagger ended a charming story about a local diner that had named a sandwich after him (“I’ve never had a [expletive] sandwich named after me! I’m very, very proud”), I did not quite buy his assertion that he, Keith and Ronnie were going to go enjoy one together after the show.

Some of that fractured feeling is likely due to the absence of the great Charlie Watts, the band’s longtime drummer who died in 2021; the Hackney Diamonds Tour is the Stones’ first North American stadium tour without him. His replacement, Steve Jordan, does about as good a job as anyone could — like Watts, he balances a rock drummer’s power with a jazzy agility — and his presence never overwhelms. Though they are surrounded by plenty of talented backing musicians, the staging makes it clear that the Rolling Stones are now a trio.

The night’s breakout star, though, was Chanel Haynes, a backing vocalist who took center stage to sing with Jagger during two of the night’s best performances. Haynes — who played Tina Turner in the West End production of the jukebox musical “Tina” before joining the Stones’ touring band in 2023 — ably filled the shoes of the mighty Merry Clayton on a blazing “Gimme Shelter,” and sat in for Lady Gaga on “Sweet Sounds of Heaven,” matching the megawatt intensity of her “Hackney Diamonds” cameo. Though Haynes could be velvety soft when the song called for it, at her most impressive she sang with a low, grumbling hunger that often swelled into ferocity, as if she were taking big, meaty bites out of the songs.

Jagger, for his part, delivered many of his lines in his signature bark: The second song, a somewhat slowed down and blues-ified “Get Off of My Cloud,” was transformed by his almost scat-like delivery. But in fleeting moments — including a few falsetto runs — he showed that a certain tenderness in his tone remains intact.

That was most apparent on a gorgeous rendition of “Wild Horses,” the song that gained inclusion in the set by winning the nightly online “fan vote.” For so much of this show, the Stones effectively proved they could outrun age, irrelevancy and all the other indignities that time brings to mere mortals. But here they settled into something more contemplative, elegiac and vulnerable, and the show was better for it.

At a time when their few remaining peers are wrapping farewell tours and bands that have been together for half as long are running on fumes, the Stones are an anomaly. It’s not that their show is devoid of nostalgia, but it’s not coasting on it either. They don’t look like they did in the ’70s — who does? — but when their sound is gelling they are able to tap into some kind of eternal present. For better or worse, they seem intent to be the last band of their generation standing, to ride rock ’n’ roll all the way to its logical endpoint. Astoundingly, they don’t sound like they’ve reached it yet.