Like last season’s Lincoln Center production of My Fair Lady, the Roundabout Theatre Company’s current Broadway revival of Kiss Me, Kate, directed by Scott Ellis and opening tonight at Studio 54, had its share of finessing to do, bringing an acknowledged work of stage musical genius from a less gender-enlightened era in line with modern sensibilities. We can put that concern aside – whatever occasional shortcomings befall this mostly terrific revival, a spanked, put-upon heroine isn’t one.

Kelli O’Hara and Will Chase are so evenly matched – in performance, talent and temperament – that it’s hard to imagine a more finely balanced battle de deux. Whatever spanking goes on in this musicalized update of Shakespeare’s The Taming of the Shrew, well, each gives as good as she gets. And the roughhousing is so vaudeville cartoonish that the bum-bruising (his and hers) could trigger nothing more than a Carol Burnett Show flashback.

But first, the musical itself: First staged in 1948, with a book by Sam and Bella Spewack and music and lyrics by Cole Porter – a Porter masterpiece, in fact – Kiss Me, Kate follows the on- and off-stage lives of Fred Graham (Chase) and Lilli Vanessi (O’Hara), he a director, producer and actor, she an actress and star. Once married, the two battling egos are reunited for a new production of Shakespeare’s The Taming of the Shrew, so we are privy to the backstage bickering that inevitably finds its way onto the Shakespearean stage.

There’s a secondary romance and some Damon Runyon-esque gangstery, but more about that later. For now, let’s talk Porter. Kiss Me, Kate has some of the best songs the great man ever wrote, which means Kiss Me, Kate has some of the best songs anyone ever wrote for the stage.

Here are a few: “So In Love,” “Too Darn Hot,” “Where Is The Life That Late I Led,” “From This Moment On,” “Brush Up Your Shakespeare,” and that perennial favorite of cabaret divas everywhere, “Always True To You In My Fashion.”

The latter, here sung by Broadway ingenue Stephanie Styles playing the show’s Broadway ingenue Lois Lane, is an ode to a young woman’s mercenary do-anything with-anyone bid for self-preservation and advancement. Styles sings this brilliantly and intricately rhymed lyric as a no-apologies Cri de Coeur, and a terrifically funny one at that.

Despite Ellis’ initially ambling staging of the musical’s introductory number, “Another Op’nin’, Another Show,” in which the “cast” of Shrew arrives on the onstage backstage, greeting one another and sharing in the excitement of first rehearsals, this production of Kiss Me, Kate takes a bit more time than perhaps it should building steam (though that’ll soon come, and then some). The Fred & Lilli “Wunderbar” duet is pleasant enough, but lacks the smoldering, underlying heat we need to feel from these two estranged beloveds.

For me, the production takes full flight with “I Hate Men,” about midway through the first act, when O’Hara (as Lilli as Shrew‘s Kate) delivers a full throated and beautifully arch takedown of what later generations would simply call patriarchy. “Kate” delivers this song with utter conviction – no sense of the I’m just a silly girl spouting off that earlier productions might have presented.

In fact, despite some script doctoring by the talented composer-lyricist Amanda Green (she performed similar updating duties on her father Adolph Green’s On the Twentieth Century for a 2015 Roundabout revival), this Kiss Me, Kate feels as modern as anything from ’48 can. The updates seem mostly in tone and performance (and thankfully so – a “guns don’t kill people” joke proves just how hokey these explicit updates can be; better is Kate’s late-show song “I Am Ashamed That Women Are So Simple” shifting to “I Am Ashamed That People Are So Simple”).

More schooled Porter experts might catch other modernizing changes sprinkled here and there, but the feel of gender equality is unmissable to anyone. O’Hara’s Kate is every bit the match for Chase’s Petruchio, her Lilli step in step with his Fred. Part of that is, no doubt, the strength of these two performers – O’Hara has delighted Broadway audiences in The Bridges of Madison County, The King and I and The Light in the Piazza, to name a few, while Chase, perhaps most widely known for his TV roles on Nashville, Sharp Objects and Stranger Things, has long since been one of Broadway’s leading men with Something Rotten!, The Mystery of Edwin Drood, Billy Elliot and Miss Saigon, again to name a few.

In the supporting roles, Corbin Bleu (Broadway’s Holiday Inn, TV’s Franklin & Bash) is all gusto as the gambling hoofer who sets in motion the mistaken identity twist that has two clownish gangsters (John Pankow, Lance Coadie Williams) trailing star Fred both onstage and off – the musical’s single most dated trope, funny here and there, creaky everywhere, and more successfully exploited later in My Favorite Year.

As Bleu’s beloved, the defiantly generous Lois Lane, Styles is a charmer in her Broadway debut. Her squeaky-wheel Noo Yawk delivery is a nod to every dreamer from Judy Holliday in Born Yesterday to Faith Prince’s 1992 turn as Adelaide in Guys and Dolls. There were a few moments when the orchestrations threatened to overpower even her big voice, but no matter: If Styles isn’t in quite that lofty company of the world’s Faith Princes just yet, she seems to be on her way.

Other dazzlers in this production include Bleu’s tap dancing routines, choreographer Warren Carlyle’s sultry-goes-blazing “Too Darn Hot” performed by the exceptional ensemble, the vibrant, velvety costumes of Jeff Mahshie (and kudos for the touching tribute to the late Marin Mazzie, whose hat from an earlier production of Kate makes an appearance), and David Rockwell’s duel sets of backstage realism for the Lilli and Fred scenes and cheeky, rather lovely watercolor flats for Kate and Petruchio. The design, like much else in this Kiss Me, Kate, keeps perfectly true to the fashions of Cole Porter having a blast with William Shakespeare.