Even though he ranks among America’s foremost living playwrights, John Guare’s work isn’t done nearly often enough in New York. This season’s Broadway revival of “Six Degrees of Separation” will be that play’s first major New York staging since the original production closed in 1992. That struck me as reason enough to catch the Florida Repertory Theatre’s revival of “The House of Blue Leaves,” an identically important play that received a big-ticket Broadway revival in 2011 (David Cromer was the director, Ben Stiller and Edie Falco the stars) that inexplicably failed to ring the box-office bell. That version was outstanding in every way—but so is this one, directed with unshowy, profoundly comprehending skill by Chris Clavelli.

That’s no surprise, since Florida Rep is one of America’s top regional companies. But “The House of Blue Leaves,” first performed in 1971, is a fearsomely and famously tricky play to bring off, for it illustrates Mr. Guare’s pithy dictum that “farce is tragedy speeded up.” It’s the story of Artie (Greg Longenhagen), an inept blue-collar songwriter from Queens whose wife, Bananas (Rachel Burttram), is clinically depressed beyond hope of cure. He’s fallen in love with Bunny (Carrie Lund), his downstairs neighbor, a brassy golddigger who believes, God knows why, in the commercial potential of Artie’s songs (one of which rhymes “comical” with “yarmulke”) and wants him to send Bananas to an insane asylum, go to Hollywood and make his fortune—meaning her fortune.

As is his wont, Mr. Guare plays this dire situation for belly laughs, mixing in such unlikely supporting characters as a trio of ditsy nuns (Viki Boyle,Michelle Damato and Jason Parrish). But you are never allowed to lose sight for long of the dark desperation of Artie and Bananas, and when things go definitively sour, first with a bang and then a whimper, the laughter gives way to gasps—and tears. Imagine, if you can, an episode of “The Honeymooners” rewritten by Eugène Ionesco: That’s “The House of Blue Leaves.”

Mr. Clavelli and seven of the 11 members of his cast are longtime members of Florida Rep’s regular core ensemble. They’ve worked together repeatedly, and it shows: This is the kind of production whose uncanny stylistic unanimity helps to weld together the play’s seemingly disparate parts. To single out any one of the actors for particular praise would do the others an injustice, for they are all marvelous. Their performances are at once deliberately, anti-naturalistically broad—that, too, is Mr. Guare’s way—and as true to felt life as Ray Recht’s set, a pitifully shabby apartment that looks as though it hasn’t seen the wet end of a mop for at least a decade.

The best American regional theater is as good as it gets, Broadway not excluded. But if I had to pick one show from the past few seasons to epitomize its excellence, it might well be Florida Rep’s “House of Blue Leaves.” It’s one of the finest stagings of a John Guare play that I’ve ever seen, anywhere.

Mr. Teachout, the Journal’s drama critic, is the author, most recently, of “Satchmo at the Waldorf.” Write to him at tteachout@wsj.com.