How Tony Bennett and Lady Gaga got a special kick out of each other

On the surface, Tony Bennett and Lady Gaga certainly appeared like the oddest of couples.

That was most definitely the case when the “I Left My Heart in San Francisco” crooner paired up with the shock diva — who sang “He ate my heart” on 2009’s “Monster” — for their first collaborative album, 2014’s “Cheek to Cheek.”

The two had previously worked together, on his 2011 “Duets II” LP, playfully partnering on “The Lady Is a Tramp,” the same year that Mother Monster had gone full-on zombie in her “Born This Way” video.

That was about as far as you could get from Bennett’s classy, debonair style. I mean, did you ever see the man not in a perfectly tailored suit?

Indeed, about the only thing that Bennett — who died at 96 on Friday after a long battle with Alzheimer’s disease — seemed to have in common with the nearly 60-years-younger Gaga was that they were both native New Yorkers.

But after Gaga’s career took its first hit with the relative flop — by her standards — of 2013’s “Artpop,” the singer needed to wipe away the artifice and remind the world about the talent underneath the skull makeup.

And “Cheek to Cheek” — featuring jazz standards by the likes of George Gershwin, Cole Porter and Jerome Kern — was a cred-boosting affair that proved that, at that moment, it was Gaga who needed Bennett more than the other way around.

It went on to win a Grammy for Best Traditional Pop Vocal Album in 2015, when there seemed to be absolutely nothing “traditional” about Gaga.

If there was an award for Cutest Couple On The Red Carpet at the 2015 Grammys, they would have won that too.

And when they performed Irving Berlin’s “Cheek to Cheek,” you could just feel the love between them.

“It was magic, because there was such an obvious affection both ways,” longtime Grammy producer Ken Ehrlich told The Post. “It was definitely genuine.”

Their “love affair,” as Ehrlich described it, was just what Gaga seemed to need to get the fervor back that was missing from “Artpop.” Indeed, 2016’s country-flavored “Joanne” felt like a passion project that set her up for Oscar glory in 2018’s “A Star Is Born.”

Thus, a star was reborn.

By the time they reunited to record 2021’s “Love for Sale” — when Bennett won the last of his 19 Grammys last year — his health was failing following his 2016 Alzheimer’s diagnosis.

“It was a gift,” Gaga told USA Today in 2021 about making the album. “It’s a gift that I will hold in my heart ’til my last breath. My time with Tony has changed me forever. Frank Sinatra said he was the best singer in the world, and I don’t think Frank lied.”

And when it was Gaga’s turn to be there for Bennett, she did just that. She lovingly carried — make that, willed — him though his emotional final live performance at NYC’s Radio City Music Hall in August 2021.

“I tell Tony every day that he saved my life,” Gaga told Parade in 2014.

And she saved his right back.