About an hour into Billy Joel’s record-breaking 150th concert at Madison Square Garden, the entertainer departed from his vast catalog of hits and launched into the Rolling Stones’s “Start Me Up.” Affecting an overstated vocal rasp and strutting like a peacock on amphetamines, Mr. Joel delivered a dead-on impersonation of Mick Jagger’s geriatric bad-boy shtick.

While I’m sure it was an entirely affectionate gesture, the bit offered a reminder that though rock stars can have some difficulty aging gracefully, skilled musicians tend to face less of a burden. Unlike Mr. Jagger, who just turned 81, the 75-year-old Mr. Joel is both; and for the past 10 years, the Bronx-born, Long Island-bred piano man has been delighting hometown crowds with polished but earthy performances, packed with singles that remain pop staples decades after their releases.

At Thursday’s show, billed as the last in this residency, that crowd characteristically spanned generations, from Mr. Joel’s peers to a substantial number of Generation Z fans. The latter included my nephew, who was born years after the singer/songwriter released his last full album of pop songs, 1993’s “River of Dreams,” but still knew every lyric to the more than 20 tunes (not including a few covers) performed over roughly two and half hours — and, if I may boast, could identify most within a couple of chords.

Where the lyrics were concerned, at least, he wasn’t alone: From the opening anthem, “Miami 2017 (Seen the Lights Go Out on Broadway)” — one of a few New York-themed numbers in the set — through an exuberant five-song encore, many in the audience sang along enthusiastically. Wrapping the pre-encore set with “Piano Man,” Mr. Joel allowed his admirers to croon a chorus on their own.

Casual-natty in his custom black jacket and shirt, the star spent most of the evening at his signature instrument; now and then, a video screen looming above the stage would zoom in on his fingers tickling the ivories, displaying enduring agility and gusto. Yet the septuagenarian also proved savvy in reserving his energy, apportioning showcases to individual band members so that he could have moments out of the spotlight.

Mr. Joel singled out these colleagues with praise and pride, among them Crystal Taliefero, a singer and multi-instrumentalist who buoyantly channeled Tina Turner during a medley of “River of Dreams” and “River Deep, Mountain High.” The similarly multifaceted Mike DelGuidice sang Puccini’s “Nessun Dorma,” enabling Mr. Joel to show off his classical chops.

As has usually been the case with Mr. Joel’s shows, which have drawn musical guests ranging from Miley Cyrus to Tony Bennett to violinist Itzhak Perlman — not to mention a parade of other classic rock icons — there were surprise appearances. Mr. Joel’s two younger daughters joined him for “My Life,” with 6-year-old Remy Anne perched demurely atop the piano while her sister Della Rose, 8, led a cheering crowd in singing and clapping.

“Wow — I guess it’s her life now,” Mr. Joel quipped.

Jimmy Fallon was another cheerleader, as the comedian and talk show host popped in to note that “Madison Square Garden has the Knicks, the Rangers, and Billy Joel.” The teenage girls seated behind me were far more excited when the Guns N’ Roses frontman, Axl Rose, turned up, sporting a glittering blazer and dark sunglasses; if his caterwauling through the Paul McCartney and Wings tune “Live and Let Die” and AC/DC’s “Highway to Hell” made me hope that there weren’t any service dogs in the venue, Mr. Joel and his band seemed to have fun.

Mr. Rose returned to help the main attraction close the encore with “You May Be Right.” As Mr. Joel had suggested earlier, though, this wasn’t necessarily so long for good. “There’s no place like it,” he had said, surveying the arena. “The band loves it; the crew loves it. We’ll come back.”