If self-effacement were a martial art, Tally, the very unconventional heroine of Abby Rosebrock’s new play, “Lowcountry,” would merit a black belt. Arriving at the home of a man she has just met on Tinder, she begins making small talk about warlords, environmental rape, and the surveillance state, then pauses to admit, “I’m a neurotic, obsequious coward.”

Getting comfortable with her date, David — who has his own issues — she continues: “I’m very self-righteous but I have no follow-through. … To be so full of rage, at the goddamn machine but so paralyzed … I have enough self-awareness to know, at my core I’m a dithering, spiritually weak, fragile … craven-ass white woman, David.”

You may suspect this lady is protesting too much, but you don’t know the half of it. In David and Tally, Ms. Rosebrock has crafted two of the most unpredictable characters and one of the most unlikely couples we’ve seen on New York stages in some time, and their journey is full of twists that can be funny or horrifying — or both at once.

That journey unfolds over the course of just one evening, though each party brings along a lot of dark history. David, played by an excellent Babak Tafti, is a former high school teacher and coach who lost both positions in a scandal that landed him under house arrest for a spell. Born nearly 40 years ago in an unspecified foreign country — the script indicates he is “brown” — and then adopted, he has always, one senses, been something of an outsider in his small town in South Carolina. 

Tally, also in her late 30s, grew up in the same community, but moved to Los Angeles with dreams of becoming an actress. Having found little success in that pursuit, she has supported herself through gig work, while maintaining a personal life that could generously be described as unsatisfying. She is desperate to become a mother — or so she says, repeatedly.

Brought to life in a fearless, devastating performance by Jodi Balfour, Tally eats the pasta David has prepared for her with relish, but is more interested in his wine; by halfway into this one-act piece, she is tipsy enough to talk with her mouth full, and her level of intoxication increases steadily from there, to David’s growing concern.

Yet however sloppily drunk Tally may seem, the events that follow make us continually question to what extent she has truly lost control. It becomes more and more apparent that she has come to meet David with an agenda, though for all her seeming candor, even when she’s sober, we’re never entirely certain what it is — or if she’s quite sure herself.

Under the whip-smart direction of Jo Bonney, Mr. Tafti and Ms. Balfour capture both the very different ways their characters have been shaped by misfortune — David carries a profound sadness, while Tally has sustained a distinct hunger — and the wounded but stubborn humanity they share. Ms. Rosebrock’s writing, at once piquant and deeply compassionate, encourages empathy even as it titillates.

There is a third, less sympathetic character, Paul, David’s sponsor in a court-ordered program; we hear him speak in a phone conversation early in “Lowcountry” and then meet him briefly near its end. Played by an earthily menacing Keith Kupferer, Paul proves central in a final passage that’s as bleak and shocking as anything else in the production.

It’s a credit to the playwright, director, and actors that “Lowcountry” nonetheless doesn’t leave us fully defeated, any more than it does David or Tally. You may even exit the theater with a new sense of regard or hope for someone you know, and that’s as worthy a gift as any work of fiction could provide.