The small Southern town that’s the setting for Tennessee Williams’s 1957 play “Orpheus Descending” is the kind of place where barking dogs can be heard chasing escaped convicts before ripping them to shreds. It’s a community where men are encouraged to be bigots and bullies, and women who aren’t able to repress their moral and sensual instincts can easily wind up either dissipated, like the self-described exhibitionist and vagrant Carol Cutrere, or disappointed, like Lady Torrance, an Italian immigrant who was married off to an old racist after her bootlegger father was burned alive trying to save his wine garden from the Ku Klux Klan.

So when a good-looking, guitar-wielding drifter with the promising name of Valentine Xavier wanders into town, it’s not long before feathers are ruffled, and not just among the clattering hens who seem to make up the majority of the female population. It’s Carol who latches onto Val first, recognizing him from one of her wild nights out. But when he turns his attention to Lady, in hopes of getting a job in her mercantile store, both of their fates are sealed, and not for the better.

Although not a success during its initial Broadway run, Williams’s spin on the Greek legend of doomed lovers Orpheus and Eurydice fared somewhat better in a 1989 revival directed by Peter Hall and starring Vanessa Redgrave as Lady and Kevin Anderson as Val. A new production, at Brooklyn’s Theatre For a New Audience, finds those roles inherited by stage and screen veteran Maggie Siff and Pico Alexander, who are supported by an excellent ensemble under Erica Schmidt’s unflinching direction.

Williams drafted his “Orpheus” from the seeds of an earlier, more idealistic play, “Battle of Angels.” As the renowned critic and Williams biographer John Lahr, who served as dramaturg for this production, has noted, the character of Val was initially conceived as “a hunted primitive saint, an agent of change, rattling the cage of propriety.” By the time “Orpheus” was completed, this hero had become “a jaded sensualist” and “an embodiment of (Williams’s) moral exhaustion.”

Lady, of course, belongs to a sizable line of thwarted and unfulfilled women who fall for such inconvenient men in Williams’s catalog. But the bond she forms with Val, as portrayed in this staging, can be as tender as it is tenuous and desperate. Ms. Siff, known to television audiences for her roles in “Mad Men,” “Sons of Anarchy,” and “Billions,” gives a performance of sinuous wit and ferocious resolve, showing us the life force that burns beneath Lady’s bitter frustration and thus making her tragic arc sting all the more sharply.

Mr. Alexander’s rangy, soft-spoken Val is a quietly unsettling presence from the moment he walks onstage, seizing the flustered attention of the womenfolk who have also regarded Lady as an exotic outsider. “They say that a woman can burn a man down. But I can burn down a woman,” he warns Lady. The line, like some others in the play (and the great playwright’s oeuvre, frankly), could easily be played as camp, but the young actor’s easy sobriety and unmannered intensity make it fly.

Ms. Schmidt draws similarly nuanced and dynamic turns from the other players. Michael Cullen blends menace with decrepitude as Lady’s husband, who emerges as an even more malignant figure than she thought he was, while Brian Keane brings a heartier but artfully shaded venom to the local sheriff. Ana Reeder lends comic relief, and poignance, as the sheriff’s restless wife, who uses her artistic aspirations and talk of visions to try to forge her own connection with Val.

Yet it may be Julia McDermott’s dissolute, blazing Carol who most vividly represents the futile yearning for escape — or freedom, as it’s more commonly referred to in the play — at the core of this “Orpheus.” In capturing that spirit, this production will leave you both strangely sated and deeply unsettled.