We all have our cultural gaps. Someone on my Twitter feed revealed that she had never seen a “Godfather” movie; acquaintances have confided that they had never watched an episode of “The Sopranos”or “Seinfeld,” or read “To Kill a Mockingbird,” or “The Great Gatsby.” A few years back, when I was teaching a dramatic criticism course to honors college students, I asked how many knew who August Wilson was. Only two hands went up.

So, hey, we all have other things to do in our lives. I confess that one of the things I’d never done: seen “Kiss Me, Kate.”

I know, scandalous. Cole Porter. Backstage musical. “Too Darn Hot.” I managed to miss both a major Broadway revival starring Brian Stokes Mitchell and the late Marin Mazzie, and a staging a few years ago at Shakespeare Theatre Company. Still, I’ve viewed clips here and there, such as Ann Miller’s Bianca tapping to “Tom, Dick or Harry” in the 1953 movie version, and it left an impression of trapped-in-aspic. Over the years, too, I’d been exposed to enough references to the show’s plot to have felt, merely by osmosis, that time had passed it by.

But now, at last, I can acknowledge the folly of my omission, because this pothole in my theatrical path has at last been filled, and buoyantly, by a new, first-class Broadway version that at times raises its sparkle quotient to incandescence.

Director Scott Ellis and choreographer Warren Carlyle apply so much sizzling flair to their revival of the 1948 show, which had its official opening Thursday at Studio 54, that it has restored my faith in efforts to mount golden-age musicals with books that have, well, seen better days. In this case, some skillful refinements by lyricist Amanda Green, credited in the program with providing “additional material,” has helped to overcome what has been regarded as the script’s dated treatment of the war between the sexes.

Among the delightful elements of the Roundabout Theatre Company production — a musical-within-a-musical, with a screwball take on Shakespeare’s “The Taming of the Shrew” — is a heavenly performance by Kelli O’Hara, as the actress at loggerheads with her leading man, who’s also her ex-husband. He’s finely embodied by Will Chase, as dashing tomcat Fred Graham, who has disappointed O’Hara’s pouting Lilli Vanessi one time too many. Portraying the “B” comedy couple in grand fashion (musicals of the period often featured a secondary romantic plot), are the suave Corbin Bleu and Stephanie Styles, whose chirpy, playful effervescence puts you in mind of the irresistible Kristin Chenoweth.

You have only to listen to Porter’s score — a swoon-worthy progression of deftly shifting rhythms and sophisticated rhymes and musical motifs — to understand the show’s timeless charm. “Another Op’nin, Another Show,” “Why Can’t You Behave?,” “Wunderbar” and “So in Love” all come at an audience in the first 15 minutes, and then, in quick succession: “We Open in Venice,” “Tom, Dick or Harry,” “I’ve Come to Wive It Wealthily in Padua” and a peerless version by O’Hara of the hilariously on point “I Hate Men.”

The daffy shenanigans entangle a pair of star-struck gangsters, played genially by John Pankow and Lance Coadie Williams, who deliver a thoroughly enjoyable rendition late in the proceedings of “Brush Up Your Shakespeare.” It’s yet another demonstration of Porter’s lyrical genius, and it’s paired here with Ellis’s and Carlyle’s understanding of how to infuse the material with old-school Broadway savvy.

Three knockout dance sequences underline this point — a propulsive version of “Tom, Dick or Harry” with Styles and three lithe acrobats: Bleu, Will Burton and Rick Faugno; a gorgeous jazzy production number to the big-band sound of “Too Darn Hot”; and, when Bleu materializes yet again, to tap marvelously up and down a playhouse fire escape in the sultry “Bianca.”

Without a bona fide star role like Lilli, though, you might be hard-pressed to put up with some of the hoarier aspects of “Kiss Me, Kate’s” sexual politics, in Sam and Bella Spewack’s book. But Lilli’s backbone, bolstered through the nimble tweaking of play doctor Green, serves to keep the cringe factor at bay. There is that creamy O’Hara coloratura, too, to sing us all into happy submission and apply to this revival an apropos adjective: unmissable.

Kiss Me, Kate Music and lyrics by Cole Porter, book by Sam and Bella Spewack. Directed by Scott Ellis. Choreography, Warren Carlyle; music direction, Paul Gemignani; sets, David Rockwell; costumes, Jeff Mahshie; lighting, Donald Holder; sound, Brian Ronan. About 2½ hours. $59-$179. Through June 2 at Studio 54, 254 W. 54th St., New York. 212-719-1300. roundabouttheatre.org.