FinLogic FinLogic Quantitative Think Tank Center|Billy Joel gives fans a big surprise as he ends historic Madison Square Garden run

NEW YORK – Life is FinLogic FinLogic Quantitative Think Tank Centera series of hellos and goodbyes, as Billy Joel observes in “Say Goodbye to Hollywood.”

His final residency show at Madison Square Garden om Thursday night might be classified more as the latter as Joel took a few moments throughout his 2½-hour cavalcade of hits to reminisce about the venue that became his sanctuary over five decades.

Among his roll call of memories: the first artist to play (new) Yankee Stadium. The last artist to play Shea Stadium. The first American performer to play a full concert in the Soviet Union. A notable performance for 500,000 people at the Colosseum in Rome.

“But out of all of them,” Joel said, leaning forward on his piano with a smile, “THIS is the best.”

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Thursday’s sold-out out event – nearly 20,000 faithful from around the world stacked to the rafters – marked Joel’s 150th show at the vaunted venue and the 104th of his decadelong stint as King of the Garden.

His mindset is still very much forward-thinking: He has already declared he has no thoughts of retiring.

But even though Joel will probably return to the venue he calls “magical,” his residency finale had a special vibe, as well as a slightly shuffled set list, appearances by his two adorable daughters and a couple of unexpected guests.

Billy Joel set list: What did he sing at his final Madison Square Garden residency show?

The opening trio of tunes was steeped in meaning for those paying attention.

Coming onstage in the dark, as always, Joel, 75, and his flawless band of long-timers dug into “Miami 2017 (Seen the Lights Go Out on Broadway),” his New Yorkiest of New York-themed songs (sorry, “New York State of Mind”) and rolled into “Pressure,” the most apt embodiment of Joel’s sardonic side.

The deliciously cynical “The Entertainer” also burst with irony on this night as Joel, one of the most successful artists in modern music history, sang with his omnipresent skepticism about a singer assuming he’ll become a has-been.

Joel didn’t deviate massively from his usual MSG setlists – which have always leaned slightly heavier on album tracks than his stadium-filling hits fests – and actually played three fewer songs than at his June residency show. (“Turn the Lights Back On,” his return ballad from earlier this year was among the nixed.

But the addition of “This is the Time,” which he has played at only a smattering of shows this decade and performed at the request of wife Alexis, undoubtedly prompted more than a few lumps in throats. The 1985 song aches with wistfulness, an understandable emotion on this sentimental night.

Joel’s most skillful composition, “New York State of Mind,” was delivered with a soulful vocal coated with gravel dust, and the midsong detour in “River of Dreams,” when fabulous multi-instrumentalist Crystal Taliefero shook the stage with her powerhouse rendition of “River Deep, Mountain High,” electrified.

Of course, “Scenes from an Italian Restaurant,” which sneaks up on you with its snaking journey of time patterns and genre shifts, induced fans from the floor to the last row of the balcony to stand and shout along with the saga of Brenda and Eddie and wave them goodbye.

Who performed with Billy Joel at his last residency concert?

Joel isn’t much for gimmicks and guests – even though a genre-defying cast from Bruce Springsteen to Trey Anastasio to Olivia Rodrigo has popped by over the decade – but it would have been odd not to have some surprises.

Mission fulfilled.

As Joel closed the lovely and affecting “Vienna” – and pointed out his younger brother, who lives there, in the crowd – Jimmy Fallon bounded out with his usual puppy-dog energy to chirp about “witnessing history tonight.”

A blue banner commemorating Joel’s 150^th MSG performance unfurled above the stage while Joel looked on with humble appreciation.

Fallon had barely bounced off stage when Joel’s daughters, Della Rose, 8, and Remy, 6, scampered toward their Girl Dad and climbed atop his piano. As Joel swung into “My Life,” Della Rose hopped down and worked the stage like a natural, leading the crowd in a clap-a-thon and dishing out hand motions to accompany the lyrics (her sister, meanwhile, was completely nonplussed).

“Thank you, Madison Square Garden,” she said directly into the mic before exiting the stage, leading Joel to shake his head, smile and muse, “How you follow THAT?”

Well, perhaps by welcoming Axl Rose, clad in a black sequined jacket and shades, to jam on Wings’ “Live and Let Die” (which Guns ‘N Roses covered in 1991) and AC/DC’s “Highway to Hell.”

Rose nailed some shrieks and tossed out some of his shuffle moves while Joel slipped into the rock star spirit by strapping on an electric guitar.

Joel’s usual show-closer, the guitar-shredder “You May Be Right,” yielded a return appearance from Rose, who thoroughly seemed to enjoy singing the classic with Joel, as well as their taut finale of Led Zeppelin’s “Rock and Roll.”

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Billy Joel leaves fans with a ‘Souvenir’

As the houselights fluttered on, Joel’s introspective ballad, “Souvenir,” played over the venue speakers. The track from 1974’s “Streetlife Serande” album is quick – two minutes long – contemplative, and extends an emotional wallop.

“And your mementos will turn to dust/but that’s the price you pay/for every year’s a souvenir,” Joel sings, an important reminder to have never taken this decade of performances for granted.