There’s something daunting, or potentially a little twee, about an update of Homer’s epic “The Odyssey” set in modern-day Harlem. But Marcus Gardley’s “Black Odyssey,” which opened Sunday at the Classic Stage Company, bursts with so much energy and insight and wit that its brilliance cannot be denied.

Gardley’s new work arrives on the New York stage five years after his riveting 2018 drama “The House That Will Not Stand,” a savvy adaptation of Federico Garcia Lorca that explored a family of free women of color in 1813 New Orleans on the verge of losing their rights with the transfer of Louisiana to the United States. He shows a similar interest in history, and in crafty theater-making, with a take on the Greek epic that is both radical and utterly faithful.

Here, Ulysses Lincoln is an Afghanistan war veteran who is long presumed killed in action. His body is that of a homeless veteran mired in mental illness, but his wind wanders a hellish underworld marked by a series of trials set for him by the gods — chiefly Deus (James T. Alfred) and Deus’s brother, Paw Sidin (Jimonn Cole). Sean Boyce Johnson brings some real heft to Ulysses, a role whose heroism is marked more by endurance than action, as he navigates a series of obstacles that also parallel the history of Black America, from slavery to the Jim Crow era to Hurricane Katrina to Black Lives Matter protests. Back at home, Ulysses’s wife, Nella Pea (D. Woods), raises her teenage son, Malachi (Marcus Gladney Jr.), with the help of mortalized goddess Athena — a straight-talking woman known as Aunt Tina who quickly insinuates herself into the family’s life (and is played with scene-stealing relish by Harriett D. Foy),

Gardley has a knack for language that is both poetic and colloquial, a balance of High Art and pop culture that is breathtaking in its ingenuity. One moment, he’s dropping a reference to chess moves, Zora Neale Hurston and the Schomburg Center; the next, it’s “Euphoria” and “Super Fly.” He can also make lofty conceits accessible without dumbing them down: Here, Homer’s sirens morph into classic Motown acts like Diana Ross, Tina Turner and James Brown — while Adrienne C. Moore’s Circe performs a lyrically seductive striptease laden with juicy food metaphors as she tries to delay Ulysses’ journey. (“I don’t even need my salad tossed,” she coos.)

Director Steve Walker-Webb, who recently oversaw the sadly short-lived “Ain’t No Mo” on Broadway, strikes a similar balance here between base comedy and serious tragedy. It’s the stuff of Shakespeare, and Gardley’s play earns the comparison — and not just for his use of rhymed couplets in key scenes. Like the best of the Bard’s work, “Black Odyssey” speaks to our moment as well as to the ages.