Adrienne Kennedy has been earning acclaim for her plays for nearly 60 years, but it’s taken until now to get one of them to Broadway. While race and gender may have been factors — Ms. Kennedy, now 91, is a Black woman — so, surely, is the surrealistic nature of much of her writing, dating back to her breakthrough, “Funnyhouse of A Negro.”

It makes sense that the play that marks Ms. Kennedy’s belated Broadway bow is one of her more straightforward, naturalistic efforts. Written more than three decades ago, “Ohio State Murders” is one in a cycle of works centered on a character named Suzanne Alexander, a writer who has been widely described as an alter ego for her creator.

Ms. Kennedy herself has been vague, some might say coy, about the extent to which Suzanne’s experience reflects her own. The women share a vocation, obviously, and Ms. Kennedy is an alumna of Ohio State University, where Suzanne was a student and where she returns to speak in this one-act play — essentially a prolonged monologue, in which Suzanne periodically evokes other characters in recalling past events.

Those include a tragedy that unfolds in two parts, so that it’s even ghastlier than it initially seems. If anything as graphically awful has happened to Ms. Kennedy — who has surely seen her share of suffering and injustice over nine decades — it hasn’t been documented. 

“I was asked to talk about the violent imagery in my work,” Suzanne, played here by a six-time-Tony Award winner, Audra McDonald, says. Over a suspenseful 75 minutes, she gradually reveals its source, as director Kenny Leon sustains an atmosphere of intense foreboding.

I’ll admit here that Ms. McDonald’s undeniably impeccable work as both an actress and a singer hasn’t always moved me as it has so many other critics. I’ve too often had the sense that she is calculating a character’s thoughts and feelings rather than truly inhabiting a role. In “Ohio State,” she affects a tremulous, sing-songy speaking voice that’s an obvious impression of Ms. Kennedy’s, which can be heard in recorded interview segments played before and after the show.

That quivering, mannered quality extends to Ms. McDonald’s body language; her shaking at points suggests a severe case of arthritis, and her sporadic bursts of nervous laughter make you fear Suzanne might break down at any moment.

The performance is ultimately vindicated, though, since Suzanne’s ordeal could have left anyone so distraught, and the play’s premise is that she’s disclosing the details in public for the first time. They involve a young, white, male professor whom Suzanne met as an undergraduate, and a pair of unspeakable crimes.

The professor, Robert Hampshire, is played in flashbacks by the smoothly handsome Broadway veteran Bryce Pinkham, whose soft voice and eerily aloof manner make the character immediately suspicious. Racism is a central aspect in the play, and there are repeated references to the paleness of Robert’s skin; Allen Lee Hughes’s lighting makes Mr. Pinkham, who’s quite fair to begin with, appear almost ghostly at points. 

Beowolf Boritt’s scenic design adds to the ominous tone: Book cases are suspended at different angles over the stage and others are scattered on the ground, as if they’d crashed down during some academic apocalypse. The actors walk amongst the wreckage; they include Mister Fitzgerald, cast as a pair of more sympathetic men — including Suzanne’s future husband — and a silent, graceful Abigail Stephenson, as young Suzanne’s melancholy, violin-playing roommate, one of just a few Black women studying at the university.

We don’t meet any of the white students, but Suzanne describes them as a gaggle of snotty girls led by one Patricia “Bunny” Manley, who accuses Suzanne of stealing her watch. “If they saw us coming down the corridor they would giggle and close their door,” Suzanne remembers later. “I hated them.”

Ms. Kennedy’s heroine is understandably less interested in forgiveness — or even catharsis, for that matter — than in simply bearing witness. Her decades-old testimony has lost none of its sting.