In David Cromer’s world premiere production of Meghan Kennedy’s “The Counter,” loneliness hangs over the stage like a pall. The setting is a small-town diner, and from the moment a ponytailed waitress pours a cup of coffee for her seemingly sole customer, an older man, and begins making small talk, we sense that they share a profound sense of isolation.

That bond will eventually be tightened by a disturbing request and a tragic revelation; the first twist is made more shocking by how casually it’s delivered — by the veteran stage and screen actor Anthony Edwards, sporting a grizzled beard and an air of world-weariness in the role of Paul, a retired firefighter, as he trades lines with Susannah Flood, the actress cast as Katie, the waitress. 

Ms. Kennedy is interested in surveying the shadows that can inform everyday lives, and how they can forge unlikely connections. “What if we decide to become friends,” Paul proposes to Katie early on. “Real friends. Like we tell each other secrets. And we help each other sort through things.”

That’s basically what happens in “Counter,” over the course of 75 minutes, during which mostly soft-spoken dialogue is interspersed with quiet pauses. We meet only one other character, Peg, a local doctor who has also managed to find her way into Paul’s strikingly solitary life, played with dry warmth by Amy Warren.   

Happily, the playwright has an ideal partner in Mr. Cromer, whose flair for mining emotional depth through intimacy has helped make him one of theater’s most sought-out directors. If Ms. Kennedy’s short, melancholy slice of life would seem to offer less grist than other works he has helmed, he deftly handles the new play’s pathos and its bleak wit, and culls nuanced, moving performances from the actors.

Mr. Edwards, who last appeared on the New York stage in the Broadway production of “Prayer for the French Republic,” brings a gentle empathy to Paul without allowing us to dismiss the character as a sad sack. We see the spark that lingers in him through his attraction to Katie, which isn’t necessarily or primarily sexual. “You make good coffee with a bad machine,” he tells her, listing a number of things he has noticed while visiting the diner every morning for two years, “so you’re at least one part magic.”

Katie has been watching Paul as well, even if she hasn’t attributed mystical qualities to him, and Ms. Flood captures her own premature weariness. The co-stars enjoy an easy rapport that even becomes playful at times, though never to an extent that feels forced; “Counter” is not ultimately a tragedy, but it does focus on people who have suffered, and are suffering, and those struggles are always present, even when they’re tempered by humor. 

Mr. Cromer and his cast are ably abetted by the design team: Walt Spangler’s set feels at once cozy and vaguely desolate, and Stacey Derosier’s lighting brightens when characters occasionally indulge us with words they can’t or won’t say to each other. Both Paul and Katie grow a little bolder as the play progresses, finding courage, or at least something like hope, in each other.

“You, Katie, are … standing in front of a door,” Paul says near the end. “One that I never went through.” “The Counter” is honest enough to leave us unsure of whether Paul will ever get through that door, but it also leaves us rooting for him, and for Katie.