Jon Hudson Odom, left, as George, Maggie Wilder, center, as Dora and Kathyrn Tkel as Zoe in “An Octoroon.” (Scott Suchman)

“Hi, everyone, I’m a black playwright!” the actor Jon Hudson Odom exclaims at the outset of “An Octoroon,” Branden Jacobs-­Jenkins’s acerbically virtuosic skewering of America’s perpetually festering racial anxieties.

Before long, Odom, shedding the guise of the dramatist — who goes by the initials “BJJ” — is applying white-face makeup to portray the roles of both the altrustic heir to a broke Southern plantation and his racist archnemesis, in the “black playwright’s” new version of a 19th-century slavery melodrama. “I couldn’t find any more white guys to play the white guys’ parts,” BJJ confesses, explaining that white guys have qualms these days about embodying people who own other people. He’s unapologetic, though, about having his assistant (Joseph Castillo-Midyett) put on blackface to play house slave Pete, while the white Irish author of the original melodrama (James Konicek) materializes to smear on garish red makeup to become the Native American character, Wahnotee.

Jacobs-Jenkins, a Washington-born playwright and Pulitzer Prize finalist this year for his tragicomic workplace drama “Gloria,” is looking with a jaundiced eye in “An Octoroon” at the mechanics of “The Octoroon,” the 1859 “sensation drama” by Dion Boucicault that inspired Jacobs-Jenkins’s play. Simultaneously he’s highlighting the collective skittishness of our time over labels and racial identity and who has permission to say what about whom. By pla­cing black actors in whiteface and Latino actors in blackface and white actors in redface, he’s for­cing the rest of us to consider in the starkest terms the impact of society’s relentless color-sorting — conscious or otherwise.

It’s a fascinating comedic matrix that “An Octoroon” constructs, enlivened by Jacobs­-Jenkins’s ear for absurdity and director Nataki Garrett’s sure-handed production for Woolly Mammoth Theatre. Beginning with Odom and extending to eight other actors with evolved senses of humor, “An Octoroon” manages the wonderful trick of being smart all at once about the conventions of art in two different times. That antebellum audiences would have accepted as compelling what makes us so completely uncomfortable speaks to how far we’ve come and what we’re still trying to get past. The appearances in Jacobs-Jenkins’s play, too, of Br’er Rabbit (Jobari Parker-Namdar) remind us of the stereotypes in the old Uncle Remus folk stories and reinforce the sensation of a complicated legacy.

Even with all the “meta” filtering, “An Octoroon” can be enjoyed as in-the-know satire. Whether it’s via Odom’s funnily swaggering white hero or Castillo-Midyett expertly overdoing the groveling thing or entitled Southern belle Dora (the sharp Maggie Wilder) swanning around in costume designer Ivania Stack’s pricelessly economy-size ball gowns, director Garrett consistently keeps us entertained, even as the proceedings walk right up to edge of offensiveness.

Erika Rose is Dido and Shannon Dorsey is Minnie in “An Octoroon.” (Scott Suchman)

Along the way, we’re treated to the marvelous synchronicity of Shannon Dorsey and Erika Rose, playing a pair of slaves in Terrebonne plantation’s manor house as finely linked in comic spirit as Tom Stoppard’s Rosencrantz and Guildenstern. They’re bystanders to the main plot, which has to do with whether Odom’s pure-hearted George can manage to release from potential servitude his beloved Zoe (the excellent Kathryn Tkel). Although she’s the daughter of the plantation’s deceased patriarch, she’s also revealed to be one-eighth black — an “Octoroon,” as they say — and thus the property of the apparently bankrupt estate that may be sold off to evil M’Closky, also played by Odom.

Pivotally, amid all the soapy romantic twists involving George and Zoe and Dora, the kinship of Rose’s worrywart of a Dido and Dorsey’s tougher-minded Minnie provides the evening with its one modern relationship. We first glimpse the two in the front yard of Terrebonne, rendered by set designer Misha Kachman as a massive mansion, slightly down at the heels. In what will become characteristic poses, Dido is working diligently, in this case hilariously sweeping heaps of cotton off the walkways, while Minnie stretches out, passing on plantation gossip and oblivious to the labors that must be completed.

“An Octoroon” satisfyingly follows their progress, for with Minnie’s encouragement, they both pursue a dream of a somewhat happier life after the Terrebonne auction. What that entails and how they achieve it isn’t as important as the fact that they’re given a chance to experience their next step. It’s an outcome that Jacobs-Jenkins fashions in such a way as to explode the conceits of Boucicault’s plot and give the women a dimensionality that belies their shopworn dramatic functions. In a play in which some other characters inhabit their roles by having them painted on their faces, Dido and Minnie are maskless, and for us, seem so much more alive.

An Octoroon, by Branden Jacobs-Jenkins. Directed by Nataki Garrett. Set, Misha Kachman; costumes, Ivania Stack; lighting, Colin K. Bills; sound, Patrick Calhoun; original music, Christylez Bacon, Wytold; fight choreography, Robb Hunter; dialects, Kim James Bey. With Jade Wheeler. About 2 hours 35 minutes. Tickets: $20-$128. Through June 26 at Woolly Mammoth Theatre, 641 D St. NW. Call 202-393-3939 or visit woollymammoth.net.