As inexhaustibly original as the animated series that inspired it, the kookily brilliant “Mr. Burns, a Post-Electric Play” is the sort of once-in-a-blue-moon show that stays stuck in your brain long after it has chilled you to the bone.

It’s a witty, bizarre, thoroughly riveting inquiry into the comforting — some might say confounding — durability of pop culture, as well as a rather sweet exploration of storytelling and how our innocence as a species is rekindled every time we retell or revise an old tale. Using a single episode of “The Simpsons,” in which the cartoon parodied the 1991 remake of the movie thriller “Cape Fear,’’ playwright Anne Washburn shows us with astonishing audacity (and terrific music by Michael Friedman) what might happen if technology failed us even as the primal need to make sense of our experiences lived on.

The world premiere brings to a startling climax another vibrant season for Woolly Mammoth Theatre, which began 2011-12 with the striking “A Bright New Boise,” after years in which it unveiled talked-about works such as Mike ­Daisey’s “The Agony and the Ecstasy of Steve Jobs” — returning this summer — and Bruce Norris’s Pulitzer Prize-winning “Clybourne Park.” “Mr. Burns,” smashingly directed by Steven Cosson, artistic director of New York’s the Civilians, keeps Woolly on a trajectory as one of the most influential outposts for the best new American plays.

Surely other theater companies will clamor for “Mr. Burnses” of their own — it’s the sort of smart satire that cannot be presented in any medium better than the stage. It’s by no means a lampoon of “The Simpsons” — if anything, it holds up the program as something akin to the “Oedipus” or “Canterbury Tales” of our time. The cartoon is, rather, a vehicle for an entertaining fantasia on how the themes in art of one age might be transmuted by time and tragedy into poignant mythology in another.

Aided by a talent-stuffed cast of seven — Steve Rosen, Kimberly Gilbert, Chris Genebach, Erika Rose, James Sugg, Jenna Sokolowski and Amy McWilliams — Washburn and Cosson propel us forward nearly a century, as civilization suffers near-extinction and “The Simpsons” lives on. An unexplained cataclysm has eradicated electrical power and caused the control rods in nuclear facilities to super-heat and plants to explode, killing hundreds of millions.

The cast of Mr. Burns, a Post-Electric Play.” (Scott Suchman/ Woolly Mammoth Theatre Company/Scott Suchman/ Woolly Mammoth Theatre Company)

The opening scene, set in a campsite in which survivors hunker down, is a sometimes harrowing depiction of the struggle to ascertain what’s happened. After a stranger, played by Genebach, wanders into camp, the survivors ritually pull out address books to compare notes with him on the names of others who might be alive.

For entertainment, though, they attempt to conjure “The Simpsons,” and it’s the “Cape Fear” episode that gets them going, as if they were half-stoned college sophomores reenacting choice scenes from “Reefer Madness.”

The conceit that electronic devices of all kinds are permanently kaput allows for storytelling to revert to an oral tradition. The hitch is that human memory is short, and as the decades pass in “Mr. Burns,” the accuracy of the account of the “Cape Feare” episode fades. Irony’s half-life proves even shorter; soon, no one recalls that the program was a joke. Ragtag acting troupes of the future appropriate the tale, adding their amusingly confused ideas of what commercials might have been like, complete with utterly superfluous snippets of songs by Ricky Martin and Lady Gaga.

The evening culminates in a wild pop opera, 75 years in the future, that absurdly conflates elements of “The Simpsons,” “Cape Fear” and the long-ago nuclear holocaust. (How ecstatically conjecture and supposition take flight without electronic records!) The story comes to assume religious significance: Springfield, Marge and Homer’s home town, is enshrined as a pre-disaster paradise and, as the owner of the town’s nuclear plant, Mr. Burns — deftly caricatured by Sugg — is portrayed as a bona fide devil. In “Mr. Burns’s” surreal game of telephone, “The Simpsons” has turned into Genesis.

Washburn and Cosson leave you a little dazed with their blunt imaginative force: “Mr. Burns” is penetrating but cold, and I suspect you’ll be astounded by it more than moved. Because its reference points are patterned so strongly on the cartoon series, too, the piece might appeal most intensely to those who’ve grown up with Bart and Lisa — and theatergoers who most enjoy seeing things onstage that don’t duplicate what they’ve seen before.

As for “Cape Fear”: I wonder whether there might be a need for the characters in Act 1 to recount a bit more about the film as an aid for anyone unacquainted with it.

Cosson’s guidance of his cast would be hard to improve upon. Beginning with the superb Rosen, Gilbert, Rose and Genebach, each actor approaches the material with a rewarding sense of belief in “Mr. Burns’s” twisting reality, whether they’re portraying traumatized survivors or their descendants, or embodying “Simpsons” characters in ever more distorted get-ups. Something delightful is sparked by Rosen, for example, when he assumes in deadpan fashion the role of Homer, who can’t get it through his thick skull that as he enters a witness protection program, he must answer to a new name. With the help of the slightly sinister half-masks by costume designer Frank Labovitz, Rose, meanwhile, manages to disappear into Bart’s boyish countenance for a final, bloody showdown with Mr. Burns.

Somehow, too, Misha Kachman’s sets, skillfully lighted by designer Colin K. Bills, heightens the tension by straddling the real and cartoon worlds. His curtain and set for the climactic “Cape Fear”-emulating encounter on the river evoke the menace in Martin Scorsese’s film and the whimsy of Matt Groening’s animated sendups.

Washburn has a gift for alternative realities. She came up with an entire language and culture for her play “The Internationalists,” which set an American adrift in cultural chaos. Here, she has us traveling once again into an alien world that’s all too familiar. Touching our sensitive, doomsday nerve, and dreaming up new roles for some of our most beloved characters, she makes the post-electric electrifying.

Mr. Burns,
a Post-Electric Play

by Anne Washburn. Directed by Steven Cosson. Composer, Michael Friedman; sets, Misha Kachman; choreography, Diane Coburn Bruning; costumes, Frank Labovitz; lighting, Colin K. Bills; sound, Elisheba Ittoop; musical director, Jonathan Tuzman; fight choreography, Lorraine Ressegger. About 2 hours, 10 minutes. Through July 1 at Woolly Mammoth Theatre, 641 D St. NW. Visit or call 202-393-3939.