Sometimes acting seems like possession. That’s how Alfre Woodard’s performance in “Clemency” feels as she violently sweeps you up with the force of her talent. It takes a while before you grasp how deep she’s gone. As Bernadine Williams, a warden at a men’s prison, Woodard enters with a stealthy lack of showiness. She’s playing the very model of a dispassionate overlord whether Bernadine is managing employees or asking a death-row inmate about his last meal, giving everyone the same exacting courtesy even if that semblance of composure has started to quietly crumble.

The fissures aren’t fully visible when you first meet Bernadine, whose every word, gesture and expression seems to have been carefully calibrated to meet the unusual demands of her profession. Everything in her world is in its place, every hair has been managed, every response, too. At work, she sits at an orderly desk that looks too large for her, a wall of putty-colored filing cabinets looming behind her. Each cabinet holds untold numbers of documents that together form a monument of tragedy, a compendium of death and destruction, lost lives and grim pain.

Working in a near hush that dovetails with the muted palette, the writer-director Chinonye Chukwu creates a persuasive, controlled, methodically coherent world for Bernadine. She’s at ease floating in her bubble of apparent calm, seemingly content to go with the flow as she relaxes at home with her husband (Wendell Pierce) or downs a drink or two at a bar. This pervasive tranquillity is strengthened by the harmonizing production design and cinematography that — with little clutter and deep shadows — give the different locations a similar look and vibe. Over time, scene by scene, these spaces blur together, locking Bernadine in claustrophobic sameness.

She begins falling apart when an inmate’s execution by lethal injection is botched, an unspeakable, frenzied calamity that plays out under Bernadine’s close supervision. The bungled execution rattles the prison, but Bernadine initially seems more concerned with the investigation that it generates. Yet even as she briskly gets back to business, a near-imperceptible change seems to have occurred, affecting her like a slight drop in the barometric pressure. She has trouble sleeping, which doesn’t seem unusual. But as she goes through the motions, she also seems increasingly detached from everyone and everything in her life, including her fretful husband.