When the actor, author, director, and civil rights activist Ossie Davis introduced his play “Purlie Victorious: A Non-Confederate Romp Through the Cotton Patch” to Broadway audiences back in 1961, it had been seven years since the Supreme Court ruled against racial segregation in schools. Yet Jim Crow laws still lingered in the South, and voting rights would not be reformed on a national level for another four years.

In the playbill for Kenny Leon’s exuberant new revival of “Purlie Victorious,” the setting is listed as a cotton plantation in “the recent past,” just as it was in the original production, in which Davis starred opposite his equally venerable wife, Ruby Dee. The word “recent” is used loosely here, as evidenced by the period costumes — by Emilio Sosa — that hang center stage on a rack as the production begins so that the cast members can playfully push the fourth wall by dressing in them.

Yet Mr. Leon is also, clearly, nodding to the enduring challenges and concerns that make this production as timely as it is boisterously entertaining. The role of Purlie, an itinerant Black preacher who returns to his home in Georgia in hopes of buying the community church back from a racist landowner, is now played by Leslie Odom, Jr., appearing on Broadway for the first time since his triumphant run as the original Aaron Burr in “Hamilton.”

Purlie’s plan is to claim an inheritance technically owed to his late cousin by passing off a young woman he picked up in Alabama as that deceased relative. “White folks can’t tell one of us from another by the head,” he reasons — a line that got big laughs and applause at the preview I attended, as did other references to the foolishness of “white folks,” a term that appears 29 times in the script.

This is satire, of course, and Davis took care to offset the cartoonish bigotry and oafishness of the landowner, one Ol’ Cap’n Cotchipee — captured to comic perfection here by the redoubtable Jay O. Sanders — with a far more sympathetic character: his progressive son, Charlie. Played in the original staging by a young Alan Alda — who is among the producers of this revival — Purlie’s fellow purveyor of “integrationary ideas,” as the Cap’n calls them, is portrayed with a perfect balance of righteousness and goofiness by an adorable Noah Robbins.

As the well-intentioned but hifalutin Purlie, Mr. Odom deftly channels the extraordinary dynamism that makes him such a charismatic musical actor; nonetheless, another performer constantly threatens to steal their scenes together. That would be Kara Young, whose compelling turns in “Clyde’s” and “Cost of Living” in recent Broadway seasons only hinted at the comedic prowess she brings to the juicy role of the young lady tasked with impersonating Purlie’s cousin, Lutiebelle Gussie Mae Jenkins,.  

A woman who has never known her parents, who has spent her life being bounced from one thankless job toiling in a white family’s kitchen to another, Lutiebelle might have been a tragic figure in another context. Yet Davis, without dismissing the poignancy of her plight, made her a zesty and decidedly lustful ingénue who upends everyone’s expectations, and Ms. Young and Mr. Leon have a grand time milking her antics for optimum hilarity.

Billy Eugene Jones and Heather Alicia Simms lend frisky support as, respectively, Purlie’s brother, Gitlow, the Cap’n’s favorite field laborer — an “Uncle Tom-type Negra,” as his boss appraises him, cluelessly — and Gitlow’s spirited wife, Missy. Vanessa Bell Calloway brings a dry, elegant humor to the part of Idella, a housekeeper who has been in the Cap’n’s employ even longer and manages to outwit him at every turn.

If you’ve any doubt about how things turn out in the end, I refer you to the hero’s chosen last name. Yet if “Purlie Victorious” offers little in the way of suspense or answers to hard questions, it does provide some catharsis in the simplest and most reliable of forms: laughter.