By Jordan Wright (Photo/Scott Suchman)

A stunner of a show just rolled into town and utterly knocked our socks off. Cole Porter’s “Kiss Me, Kate,” the play-within-a-play — well, not quite, since it’s a musical — brought with it a fresh breeze to Sidney Harman Hall thanks to director Alan Paul.

Using Shakespeare’s “The Taming of the Shrew” as a baseline, Porter composed the music and witty lyrics with Samuel and Bella Spewack, two of the finest stage writers of their time, who penned many a Broadway show and Hollywood screenplay.

In this madcap creation, we are privy to the goings on backstage, where all the action is set. The storyline follows two couples who are preparing their parts for Shakespeare’s classic tale — Lilli Vanessi (Christine Sherrill, who also plays the eponymous shrew, Kate) and her ex-husband slash co-star Fred Graham (Douglas Sills, also in the role of the suitor Petruchio); and Lois Lane (Robyn Hurder, who also plays Bianca) and her gambler boyfriend, Bill Calhoun (Clyde Alves, who also plays Lucentio). Got it? They also have relationship issues. Who doesn’t?

Add in Fred and Lilli’s dressers, Hattie (Zonya Love) and Paul (T. Oliver Reed), a backstage crew, an entire chorus line, and sprinkle in a couple of rough and tumble gangsters played by Bob Ari and Raymond Jaramillo McLeod, and it’s on.

See this production for the dancing, featuring the jitterbug, leaps, high kicks and acrobatics combined with tap, waltz and rumba by the best hoofers around. Choreographer Michele Lynch co-opts every inch of real estate for each intricate routine.

See it for the steamy cavorting or see it for the singing. It will take your breath away. The audience literally squealed with delight, clapping wildly after each number. Sherrill is maddeningly captivating as Kate in the tune, “I Hate Men” and Sills grabs the spotlight in “So in Love.”

As for Hurder, the audience nearly wouldn’t let her off the stage after her first number, “Tom, Dick or Harry,” and her sizzling, negligee-clad, vamp rendition of “Always True to You in My Fashion” is not to be missed. In the second act, sultriness finds a higher bar with “It’s Too Darn Hot,” led by Paul and Hattie and augmented by the dancers.

A 10-piece orchestra, led by James Cunningham, stays true to the nifty sophistication of Porter’s music, coupling neatly to sound designer Justin Stasiw’s sound effects. And scenic designer James Noone’s 1940s-era sets of the Ford Theater’s backstage interspersed with drops depicting 16th century Italy are reminiscent of The New Yorker’s 1940s pen-and-ink illustrations of the day.

Run — don’t walk — to the box office for this one.