In Fetch Clay, Make Man, an imagined account of the real-life friendship between brash young heavyweight champion boxer Muhammad Ali (né Cassius Clay) and washed-up film star Stepin Fetchit (né Lincoln Perry), the right-hand blow Ali uses to end his rematch with Sonny Liston in the first round is referred to as the “anchor punch.” It’s more commonly called the “phantom punch,” because almost no one at the 1965 fight actually saw it—not even Ali. “Did I hit him?” he asked his cornermen after Liston went down.

Ali’s victory over Liston, among the most controversial in the history of the fight game, was captured in one of the most famous sports photographs: Neil Lefner’s shot of an angry Ali standing over a dazed, prone Liston and taunting him to get up and fight. Many sportswriters and fighters alleged that Liston—whose title Ali had taken away the year before—threw one or both of his fights with Ali. By the time of their rematch, Ali had been accepted into the Nation of Islam; members of the Nation had assassinated Malcolm X three months earlier. At the fight, Ali was under guard not just by the Nation’s security force, who feared retaliation by Malcolm X’s supporters, but by an FBI detail, too.

Will Power’s persuasive, funny, fully engrossing drama, first staged in 2010, feels oddly relaxed considering how tense this historical moment really was. Ali’s life had been threatened, but like the champ himself, Power—who performed his hip-hop solo piece Flow at Studio theatre back in 2005—chooses to worry only about his dignity. In Power’s version, the 23-year-old “Louisville Lip” has summoned the 62-year-old actor to Lewiston, Maine, the backwater that got the fight after bigger markets refused to host it, citing fears of violence and other concerns. He’s heard that Fetchit was pals with Jack Johnson, the first black world heavyweight champion, and he wants to know if Johnson ever let Fetchit in on the secret of that “anchor punch.” Silly, but a good MacGuffin. Ali really did claim Fetchit taught him Jack Johnson’s anchor punch, but I’m unaware of any accounts of Johnson ever throwing a short, chopping right hand like that. Ali might’ve just been having fun with the press, as was his wont.

Brother Rashid (Jefferson A. Russell), Ali’s bowtie-wearing Nation aide and minder, takes umbrage at Fetchit’s presence in the camp because of the content of the actor’s movies. Fetchit became the first black movie star by adopting a screen persona that would soon come to be recognized as a deeply offensive racial caricature—lazy, bug-eyed, and easily frightened. In flashback scenes, we see Fetchit cannily negotiating raises and perks with studio mogul William Fox (Robert Sicular), controlling his own destiny outside the frame while shucking and jiving in the pictures. (The show opens with a recreated excerpt from one of his films, wherein Fetchit is caught napping on the job and tells his boss that he’s not himself. It sounds heavy-handed, but it doesn’t play that way.) It’s impossible to imagine the defiant, egotistical, political Ali ever behaving like that, but Powers asks us to consider if Fetchit’s public humility, however self-serving, might’ve made Ali’s loud-and-proud, self-actualized superstardom possible.

Round House Theatre’s co-production with Marin Theatre Company benefits from a pair of extraordinary lead performances that meet the challenge of inhabiting two of the most famous men of the 20th century. Roscoe Orman—best known for playing Gordon, one of the humans on Sesame Street, for 40 years—imbues Fetchit with the wounded dignity of a broke former superstar who might feel some shame for the way he rose to the top, but damned if he’s going to let that self-righteous prick Brother Rashid see it. Eddie Ray Jackson has the even tougher job of evoking the champ, whose face, voice, and footwork will be familiar to much of the audience. (The latest Ali documentary opened just last week.) Jackson makes us believe by not going for a direct vocal impression, though he incorporates some of Ali’s sing-songy lilt into his speech. Physically, he inhabits the role beautifully: He’s broad and lean like Ali was in the ’60s, and he’s got the champ’s distinctive, wide-legged, jiglike shuffle down.

Ali’s first wife, Sonji Roi, is also a potent element in this mix. The second Liston fight came at about the halfway point of their 18-month marriage. As Roi—who was a cocktail waitress when she met the fighter who still called himself Cassius—Katherine Renee Turner captures the strain of a new celebrity spouse bristling at the expectation that she dress and behave as a modest and deferential Muslim woman.

Caite Hevner Kemp’s projected black-and-white collages of news footage of Malcolm X and Elijah Muhammad remind us of the political atmosphere outside of Ali’s dressing room, where all this domestic strife is unfolding, and efficiently dial up the Prohibition Era for Fetchit’s flashbacks. None of it, not even Jackson’s shuffling and boasting and shadowboxing, feels flashy. But it accrues into something memorable and profound. Fetchit got famous reinforcing negative black stereotypes, while Ali cast off what he called his “slave name” and told white America he didn’t need their permission or approval. To eavesdrop on this pair of titans is a privilege.

Fetch Clay, Make Man is on stage at Round House Theatre, 4545 East-West Highway, Bethesda. $10-$50..