It seemed like naughty kismet that Arizona Theatre Company’s production of “The Underpants” would happen soon after Janet Jackson’s breast-baring Super Bowl incident.

The plot of “Underpants” centers around a similar wardrobe malfunction: In comedian Steve Martin’s three-year-old adaptation of the 1911 German satire “Die Hose” by Carl Sternheim, naifish Louise Maske (played here by Julia Dion) waves to the king at a royal parade, only to have her drawers drop accidentally. A scandal ensues, complete with newspaper coverage and a string of men lusting after sweet Louise.

While Louise struggles with the ruckus and her flock of new admirers, husband Theo (Conan McCarty) — classically piggish, a low-on-the-totem bureaucrat by trade — can think of nothing but himself. He can’t see that his absurd selfishness, and a little prodding from nosy upstairs neighbor Gertrude (Peggity Price), has driven Louise to pondering a bit of deliciously deceptive infidelity.

But “The Underpants” has more in common with the farce of “Three’s Company” than the pop-culture novelty of a halftime show. Playwright Martin and ATC show director Jon Jory — a prestigious import with an impressive resume of professional theater — aim low for the laughs and come up with a hilariously enjoyable evening of ribald double entendres, comic mugging to the crowd and people who are not what they claim to be — or not be, like pitiful wooer Benjamin Cohen (Everett Quinton), a Jew who, because of sensitive times, swears he’s not. (His last name is spelled with a K, he says.) It’s a show of old-world sensibilities that sparks with energy enough for a modern sitcom.

Adaptation is a form that suits Martin just fine. Having previously worked with well-known stories like “Cyrano de Bergerac” (for the film “Roxanne”), Martin mines less-familiar roots for “The Underpants” and comes up with a 90-minute, no-intermission pleaser that shines with his broad wit. I much prefer this work to Martin’s original play “Picasso at the Lapin Agile,” with its sprawling lurches into obtuse silliness — though it’s obvious Martin has toned down the satire of Sternheim’s original “Die Hose” to give us more likeable characters. Here, Martin’s jokes are still as soft as his novellas but packed with enough bawdy bite to appeal to the sensibilities of modern audiences — even if the shock of huge, lacy knickers has given way to today’s dulling bevy of publicly flashed thongs.

Martin’s script is only made better by the performances of the seven-member ATC cast. Dion’s Louise pursues her affair with the frantic frenzy of a shopping spree contest winner, and actors Quinton and Jarion Monroe (who plays a constipated professor with a great gnashing of his teeth) are brilliantly comic.

The fun farce is played against Robert Dahlstrom’s creamy ivory and gray apartment set, its design as comically skewed as the show itself, with Tim Burton-style doors and walls and side and overhead flats covered in New Yorker-style doodles.

Those looking to find the poignancy of Sternheim’s satire will be disappointed by how Martin — a “Saturday Night Live” alum who knows the value of wringing a tasty premise for every possible ounce of comedy — has skirted his source material. But for the rest of us looking for a simple night of big laughs, “The Underpants” is worth a peek.