NEW YORK — It’s typically the job of the lighting designer to supply a luminous fade-out. But with “The Waverly Gallery,” Kenneth Lonergan’s profoundly touching account of the waning days of a woman drifting away from her family in dementia-driven confusion, an especially captivating cast member takes charge of that task, with consummate warmth and grace.

That performer is Elaine May, better known for her comedy — as half of the legendary act she performed way back when with the late Mike Nichols — than for her dramatic acumen. But onstage at the Golden Theatre, where Lonergan’s memory play from 2000 made its official Broadway debut Thursday night, May delivers a portrait so definitive, so meticulously calibrated, it would be better measured in pixels.

She plays Gladys Green — a woman modeled on Lonergan’s grandmother — who runs a modest art gallery in Greenwich Village that’s a little shabby around the edges and a vestige of a New York that thrived before gentrification barreled through the city’s lower- and middle-class neighborhoods. Gladys’s daughter, played with seemingly communicable bone-weariness by Joan Allen, and grandson (the endearing Lucas Hedges) are eager to give Gladys something to live for, other than pestering them endlessly with questions they’ve answered 20 times already. The gallery is the welcome constant, until the inevitable juncture when a landlord’s demands and an old lady’s infirmity seal its demise.

The fury her family can barely contain, over a bewilderment in Gladys that escalates by degree as the play unfolds, will immediately strike a chord if you’ve had a loved one who essentially disappeared before your eyes. The emotional progression that the characters — and an audience — experience involves guilt, too, over the impatience one tends to express at a person for whom expectations constantly must be redefined down.

Director Lila Neugebauer and company — which also includes an appealing Michael Cera, playing a New England painter whose work is the last to be exhibited in the Waverly Gallery, and a capable David Cromer, portraying the husband, Howard Fine to Allen’s Ellen Fine — generate all of the evening’s requisite tenseness. It’s a sensation that reflexively tightens the stomach: of knowing that things, even in the most cultivated of households, seem destined to end badly, in painfully messy scenes of tears and anger.

As he has shown in movies (“Manchester by the Sea,” “You Can Count on Me,”) and plays (“This Is Our Youth,” “Lobby Hero,”) Lonergan’s ear for the crosscurrents of love and recrimination, of accusation and confession, is as fine as that of any American dramatist.

His skill gets a useful workout in “The Waverly Gallery,” which may be his richest play, emotionally speaking. That Neugebauer, director previously of the exhilarating girls-soccer drama “The Wolves,” forces some unneeded window dressing onto the proceedings is unfortunate: the brick apartment-building wall that comes tumbling down between scenes blunts the rhythm of the play, and the generic scenes of New York projected onto it fight the extremely particular material with which Lonergan is working. You also wish that the staging of the narration by Hedges — outstanding as Daniel Reed, Ellen’s son and Howard’s stepson — didn’t look quite so much as if he were introducing a high school assembly.

Still, reaffirming the impression made by the recent openings of “The Ferryman” with a superior, 22-member cast, and “The Lifespan of a Fact,” starring Daniel Radcliffe, Cherry Jones and Bobby Cannavale, “The Waverly Gallery” provides Broadway audiences a splendid gallery of actors. And with her beautifully orchestrated portrayal of a woman who can’t quite figure out what of herself she’s losing, May compels audiences to the belief that they have found another great dramatic actress, at last.

The Waverly Gallery, by Kenneth Lonergan. Directed by Lila Neugebauer. Sets, David Zinn; costumes, Ann Roth; lighting, Brian MacDevitt; sound, Leon Rothenberg; projections, Tal Yarden. About 2 hours 10 minutes. $48-$149. At the Golden Theatre, 252 W. 45th St., New York. or 212-239-6200.