Rachel York and Company in Roundabout Theatre Company's "Anything Goes." (credit: Joan Marcus) (Joan Marcus/Joan Marcus)

Even the orchestra laughs along with “Anything Goes,” the jubilant, dance-your-cares-away musical comedy that just sailed into the Kennedy Center’s Opera House for a month. As the saxophones and trombones slide up and down the scale during the overture, you feel sure that a Marx Brothers-style party is about to break out.

And it does, with sex appeal and banana peels propelling director-choreographer Kathleen Marshall’s Tony-winning, shipshape revival (produced on Broadway by the Roundabout Theatre Company). The Cole Porter score is golden, of course, from the smoldering opener “I Get a Kick Out of You” to the joyful title tune, an all-hands-on-deck song and dance that earns an enchanted roar from the audience.

There isn’t much slack in the giddy book, either, which involves everything from mismatched romances to a yappy little dog going overboard during this antic transatlantic cruise from New York to England. And then there’s the dancing, which ranges from elegant Fred Astaire-Ginger Rogers courtship glides to full-stage comic extravaganzas involving closeted gypsies and fake evangelists.

The plot is blissfully, ridiculously complicated, all for the sake of ensnaring lots of improbable characters in the vaudeville wisecracks and the jolly, swoony Porter songs. As Marshall’s production unfolds and enlarges — the dance sequences are especially generous, metastasizing like big Busby Berkeley numbers — you grin and marvel that people really can still pull off this great, expansive, talent-flaunting American art form.

Rachel York is the ringleader as the slightly shady nightclub chanteuse Reno Sweeney, and it doesn’t take long to get lost in her charms. York’s happy, glamorous swagger seems imported straight from the 1930s, as do her Mae West wit and Lauren Bacall knowingness.

Roundabout Theatre Company’s “Anything Goes” is at the Kennedy Center until July 7. (Courtesy Roundabout Theatre Company and Kennedy Center/The Washington Post)

She manages to be both sweet and torchy as Reno croons “I Get a Kick Out of You” (this is a solidly sung show all around). York’s easy rhythm and ebullience drive both of the big dance numbers — “Anything Goes,” the elaborate tap affair that spreads to all three decks of Derek McLane’s handsome nautical set, and “Blow, Gabriel, Blow,” one of several occasions showing off the late Martin Pakledinaz’s smart, swanky, dance-friendly costumes as York and her backup singers shed their choir robes for fringy chorine get-ups.

Elaborate as the show is, “easy” — following York’s relaxed lead — turns out to describe most of the performances. The funny Fred Applegate has a feathery touch as Moonface Martin, a cut-rate gangster who helps Reno break up an impending marriage for a friend. (York and Applegate volley verses and punch lines like seasoned vaudevillians in their duet “Friendship.”) Josh Franklin and Alex Finke are winsome as the lovebirds Billy Crocker and Hope Harcourt, and they move smoothly through romantic Fred and Ginger dances that Marshall amplifies with pairs of lovers spinning gracefully all over the stage.

The sluggish passages are too rare and too fleeting to matter: Virtually everything is stylish, tuneful and splendidly free-spirited. The many delightful, de-lovely ingredients include Joyce Chittick’s cheerfully lusty turn as Erma, Moonface’s sometime moll. As a half-dozen muscular sailors pass Erma among themselves like an especially delectable dessert tray during “Buddie, Beware,” Chittick coos, “I love this boat.” Amen, sister.

Anything Goes

Music and lyrics by Cole Porter, original book by P.G. Wodehouse & Guy Bolton and Howard Lindsay & Russel Crouse, new book by Timothy Crouse & John Weidman. Directed and choreographed by Kathleen Marshall. Lights, Howell Binkley; sound design, Brian Ronan and Keith Caggiano. Through July 7 at the Kennedy Center Opera House. Call 202-467-4600 or visit kennedy-center.org.