Click, click, click. That’s the precision with which practically every jubilant act of irreverence registers in Shakespeare Theatre Company’s deliriously happy-making version of Carlo Goldoni’s “The Servant of Two Masters.”

Who knew that in jaded 2012 one could declare that few comic geniuses are as good as Goldoni? He died in 1793, and we all know how ephemeral taste in comedy can be. And yet this emblematic entry from the heyday of commedia dell’arte has of late spawned not one but two top-drawer adaptations: On Broadway, the uproariously updated “One Man, Two Guv’nors,” from London’s National Theatre, is nightly splitting sides courtesy of a priceless crew led by Tony-nominated James Corden.

Here in Washington, the play — in perhaps only a slightly more faithful confection, sublimely directed by Christopher Bayes — provides an equivalent bowlful of joy. Up there with playwright David Ives’s riffs on classical French comedy, director Keith Baxter’s zany treatments of Richard Brinsley Sheridan and Michael Kahn’s of Ben Jonson, this “Servant” ranks as one of the most gleeful Shakespeare company offerings of the past 10 years.

Before I go on about the bona-fide hilarity of the cast — headed by the invaluable Steven Epp, a stylistic cousin-in-clowning to the humility-projecting Bill Irwin — let me just stop here to reflect on a reference above that might have given you pause. Yes, I did connect “commedia dell’arte” and “hilarity.” In inexpert hands, the exaggerated mannerisms and stock characters of highly physical Italian comedy can be about as inviting as the Red Line on a day of single-tracking. It’s all too easy for the slapstick to lapse into calcified frivolity, the fake jabs to the head to become tedious and the ribald storytelling conventions to grow desperate. (Ever sat through the set of a stand-up comic who’s working a tad too hard?)

Rest assured: Bayes and company, egged on by adapter Constance Congdon’s buoyant script and the exuberant melodies of Chris Curtis and Aaron Halva, consistently locate Goldoni’s sweet spot. (The director originally staged the play, with a few variations in cast, at Yale Repertory Theatre in New Haven.) Interspersing the jokes with whimsical choreography and a few delightful stage effects — set designer Katherine Akiko Day and lighting designer Chuan-Chi Chan devise an enchantingly flickering prologue — the production conveys a completeness in all its assorted parts.

Okay, it’s in the nature of such carbonated mischief that some of the zaniness veers out of bounds, especially in a show that shamelessly trots out anachronisms and even encourages the actors to improvise. At the official opening Sunday night in the Lansburgh Theatre, a mildly tasteless ad-lib about Whitney Houston set off a chain reaction of actor giggling. The moment came across less as edginess than self-indulgence. (My unsolicited advice to Epp, who plays the servant of the title, Truffaldino, would be to trim the knee-jerk Federal Washington allusions by about 50 percent. Leave the so-so digs at Nancy Pelosi and Rick Santorum to the likes of Jimmy Kimmel.)