I recall the stir Once (2006) created when it played at the San Francisco International Film Festival several years ago. Since then, the stars of the John Carney directed musical film, Glen Hansard and Markéta Irglová, won an Academy Award and formed the band The Swell Season, also the name of a 2011 documentary about their offscreen romantic ups and downs while conquering the world.

Now playing at the Bernard B. Jacobs Theater, the stage adaptation is like discovering a cover version of a favorite song that’s, in its way, as good as the original. Although the success of the film depended on the chemistry of Hansard and Irglová, Steve Kazee and Cristin Milioti are also perfectly cast as Guy and Girl.

Having seen Once during its run at the New York Theater Workshop, Ben Brantley in The New York Times observed that director John Tiffany’s “exotically modest” production seemed “a little too twee . . . for the East Village. Yet on Broadway . . . feels as vital and surprising as the early spring that has crept up on Manhattan.”

Upon entering the theater, audience members come up on the stage for a pre-show that recreates an Irish pub setting. The supporting cast doubles and sometimes triples as musician/singers, actors and stage hands. David Patrick Kelly [The Warriors (1979)] is excellent as Da, Guy’s mandolin strumming father. His song, a melancholy Irish ballad, serves as a bridge into Act 1.

Glen Hansard, Markéta Irglová, Steve Kazee, Cristin Milioti

If Kazee and Milioti weren’t fine singers as well as actors, the show wouldn’t work, but they do both equally well and are completely believable as struggling musicians. Show stoppers like Hansard and Irglová’s 2008 Oscar winner “Falling Slowly” never sounded better. Underlying the romance, there’s a story about immigration, globalization and being a stranger in your home town, that adds to the poignancy.