Jimmy Fallon and James Corden put on an expected show at one of New York’s starriest spots.

After having dinner with Lorne Michaels at Emilio’s Ballato, former “SNL” star Fallon and former “The Late Late Show” host Corden “took to the stage at the secret bar in the back” of the exclusive eatery, a spy told Page Six.

The source said that in the clubby room, “The Eric Newman Jazz Band was playing, and before long, Fallon and Corden were up onstage trading Sinatra and Tony Bennett tunes!”

Corden, 47, who’s currently starring on Broadway in “Art” with Bobby Cannavale and Neil Patrick Harris, “absolutely killed it with ‘My Way,’ and Jimmy followed with a smooth, heartfelt, ‘I Left My Heart in San Francisco,’ ” we hear.

“The Tonight Show” host Fallon, 51, has a history of crooning Tony Ben

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