Very Little Known Fact: In 17th-century France, doctors dressed like Harry Potter.

I can tell you exactly when Keith Baxter’s giddy, gassy staging of The Imaginary Invalid abandons the realm of the merely funny and ascends into the sublime: It’s the rubber-legged, loose-armed, slosh-bellied turkey strut that is the dyspeptic protagonist’s first hurried exit toward an offstage bathroom, and it’s accomplished by Rene Auberjonois, the evening’s unquestioned star, with a bodily comportment that somehow manages—I say this not quite believing it myself—to wed the urgently ambulatory, the fluidly yogic, and the anxiously clenched. In other words: It’s physical comedy of the highest order, and it’s hiccup-inducing hilarious.

Now, here’s the thing: Molière isn’t easy. This is French comedy at its most ornate, a satire of a bloated, decadent society originally staged for jaded aristocratic audiences, complete with operatic divertissements and pastoral ballets interleaved with its three acts to keep the evening, er, moving. Not quite the thing for the ADD generation, really.

So it’s a wonder that the Invalid still has a pulse at all these days, much less that it capers as amusingly as it does here, with some of those ornaments still intact—vigorously pruned, to be sure, but still intact. Baxter’s production serves up brisk, abbreviated dances—Gillian Lynne is the choreographer—with tumbling Harlequins and cartwheeling Columbines giving a nod toward Molière’s debt to commedia dell’arte, along with a door-slamming, slide-whistling, eyebrow-waggling pantomime-opera recap of the play’s rising action. The latter runs five minutes or so, and it involves more breathless quick-change hilarity than Arena Stage musters in the entire two acts of its oddly enervated The Mystery of Irma Vep.

And all that’s mere window dressing. The story proper, a cheerfully coarse bit of foolery involving a hypochondriac (Auberjonois) who wants to marry off his daughter to a dweeb of a doctor’s son so he’ll always have a family of medicos on call, unfolds with a similar élan. Auberjonois’ Argan, his nightcap drooping like a half-baked pie, gargles merrily away at some nostrum as the action proper commences, then launches into a contentedly grumpy review of his apothecary bill.

Halfway through this catalog of the exotic potions and herbal enemas he’s convinced are keeping him alive, Molière brings on the requisite saucy servant—here called Toinette, and played with brisk sass by Nancy Robinette. (She’ll turn up later in disguise, doing another quick-change bit when she masquerades as a visiting doctor with the real “cure” for what actually ails Argan.)

And soon enough it’s time to meet the daughter (Gia Mora), who’s clueless about Dad’s plans for an arranged marriage and pining for a gallant stranger (Tony Roach) she met at the opera, and that old standby the wicked stepmother (Kaitlin O’Neal).

The latter’s scheming to send the girl off to a convent, the better to inherit when hubby’s medical miracles run out, and her personality swings from poisonous to sunny depending on whether her sugar daddy is within earshot—but so far, at least, her charms have kept the old fool in her thrall. (Hint: She may have a sunny smile and a damask complexion, but as packaged by Robert Perdziola’s gowns, her very best assets precede the rest of her into the room by a good eight inches.)

Adding measurably to the hilarity are Dad’s chosen bridegroom, played by Levi Ben-Israel as a stammering, stupendously gawky buffoon whose obvious disadvantages are counterbalanced by one unmistakable, ahem, endowment; the twig’s own grandly pompous quack of a pater (John Robert Tillotson); Argan’s long-suffering apothecary (David Manis) and his wife’s blithely amoral notary (Drew Eshelman); and the merrily mischievous Beralde (suavely impish Peter Land). He’s Argan’s brother, and he’s clearly inherited whatever share of sense remains to the family’s male line.

It’s all in service to a once-scandalous broadside aimed at the witch-doctors practicing what passed for medicine in the days of Louis XIV, and you’ve not really tasted contempt until you’ve been in Molière’s kitchen. With all the prime comic ingredients at his disposal, Baxter’s production is never far from a merry simmer, and by the time Beralde and Toinette have engineered a villains-foiled, lovers-united happy ending—think feigned deaths, hidden wills, and “physician heal thyself”—even the ­buttoned-up audiences at the Lansburgh will have been convinced that a hearty dose of laughter is by far the best medicine.