“Some Like It Hot,” the 1959 movie, is a comedy masterpiece. “Some Like It Hot,” the 2022 Broadway musical, is a masterwork in the art of adaptation.

The original movie, with its sterling script by Billy Wilder and I.A.L. Diamond and its top-flight cast including Marilyn Monroe, Jack Lemmon and Tony Curtis, could never be topped. When they first tried to turn the movie into a musical (in 1972), it was a giant flop. Fifty years later, the world had turned. Concepts of drag comedy and nonbinary people held a different sort of weight, and the cross-dressing escapades in the movie, as two hapless male musicians flee the mob by donning dresses and joining an all-women band, didn’t hold the same sort of comedic sway.

But when it came time to try adapting “Some Like It Hot” for the musical stage one more time, the right artists made the right choices. Songwriters Marc Shaiman (music and co-lyrics) and Scott Wittman (lyrics) cracked open the Prohibition-era big-band jazz sound and found more sparkle and fizz than a glass of fine champagne. And book writers Amber Ruffin and Matthew López tapped into something that had always made the movie more than just funny — that spark of joy in self-discovery — and made it fresh while honoring the original.

In many ways, “Some Like It Hot,” now at San Francisco’s Orpheum Theatre as part of the BroadwaySF season, is a classic Broadway musical. Director-choreographer Casey Nicholaw keeps the pace madcap and the dancing nonstop. The tap dancing alone will leave you breathless — especially the epic guns a-blazin’ chase through the halls of the Hotel del Coronado that combines tap mayhem with rhythmic door slamming.

The Shaiman-Wittman score is big, bold and brassy in ways that make it feel like Broadway of old, which is a rare kind of pleasure. In many ways, this show feels like a throwback. It’s decked out like a Broadway dream — with sumptuous Art Deco sets by Scott Pask and gorgeous ‘30s costumes by Gregg Barnes — but there’s a very contemporary heart at its center.

As in the movie, the central couple are lifelong friends and hucksters Joe and Jerry. After they witness a Chicago gangland murder, they escape certain death by disguising themselves as Josephine and Daphne and head west to California with a female jazz band called Sweet Sue and Her Society Syncopaters. Joe/Josephine (Matt Loehr) immediately falls for the lead singer, Sugar (Leandra Ellis-Gaston), a movie fan who dreams of seeing Black women like her up on the screen.

Jerry/Daphne (Tavis Kordell), on the other hand, finds liberation in wearing a dress and being with women. By the time the group reaches San Diego, Daphne has crossed a border — and not just for a crazy night in Mexico.

There are a number of love stories here — Joe and Sugar figuring out if romance can conquer deception, Joe and Jerry testing their lifelong bond in the face of major personal change, and Daphne rebuffing and then reconsidering the effervescent millionaire Osgood (Edward Juvier). Broadway musicals are often good at love stories, and this “Some Like It Hot” is really good at love stories. Act 2 includes three genuinely sweet and moving love songs: “Dance the World Away,” an elegant Astaire-Rogers number for Joe and Sugar; “Fly, Mariposa, Fly,” Osgood’s heartfelt ode to Daphne; and “You Coulda Knocked Me Over with a Feather,” Daphne’s triumphant love song for herself.

In spite of some sound issues with the 12-piece band too often overwhelming the singers, the performances burst with charm and energy. Loehr and Kordell really know how to sell a song-and-dance number like “You Can’t Have Me (If You Don’t Have Him),” and once the dresses come out, it’s only a little distracting that Daphne looks like a cross between Issa Rae and Whitney Houston.

Ellis-Gaston’s Sugar gets most of the big vocal moments, but it’s in her more intimate song about her childhood, “At the Old Majestic Nickel Matinee,” that she shines brightest. Her dreams of a more diverse world infuse the entire musical with a sense of hope that bubbles under all the glorious dancing and some very big laughs.

“Some Like It Hot” is a compassionate, wildly entertaining musical comedy that dares to fantasize about an America where race and gender discrimination can be conquered. And all it takes is good-hearted people, true love, cocktails and, of course, show tunes.

Chad Jones has been writing about Bay Area theater since 1992; theaterdogs.net.

‘SOME LIKE IT HOT’

Book by Matthew López and Amber Ruffin; music by Marc Shaiman with lyrics by Shaiman and Scott Wittman; presented by BroadwaySF

Through: Jan. 26

Where: Orpheum Theatre, 1192 Market St., San Francisco

Running Time: 2 hours, 40 minutes (including intermission)

Tickets: $55-$160.50; 888-746-1799, www.broadwaysf.com