Lili Taylor and Janeane Garofalo are sisters reunited by illness in the gratifying and affecting Broadway premiere of “Marvin’s Room,” a play that evokes the AIDS epidemic without ever naming it.

Young playwright Scott McPherson saw his dramatic comedy make its debut Off Broadway in 1991, a year before his death. It’s rooted in his own experiences looking after elderly relatives in Florida, but also influenced by time caring for his sick partner.

“Marvin’s Room” became a 1996 movie (with Meryl Streep, Diane Keaton and Leonardo DiCaprio) and has been produced frequently in smaller venues in the U.S. and abroad.

The title character, who is heard, but not seen in Roundabout’s staging at the American Airlines Theatre, is the ailing father of siblings Lee and Bessie. Director Anne Kauffman (“A Life”) lets Marvin’s presence—to the audience, just a soft wheezing from behind a bedroom door—do the play’s heavy lifting: We come to think of him as the specter of death awaiting everyone, some just sooner than others.

Among the “more” living: Taylor (“American Crime”) is Bessie, who has grown accustomed to caring for her father and dotty Aunt Ruth (Celia Weston). Garofalo, the well-known comic actress, makes a confident Broadway debut as Lee, who has her hands full caring for two sons in Ohio.

When a leukemia diagnosis drastically curtails Bessie’s ability to care for the older relatives, Lee packs up the boys and heads South, where the sisters have two decades of estrangement to unpack.

It becomes apparent that Lee and the boys are potential bone marrow donors for Bessie. One of the play’s most artfully constructed threads concerns whether sullen Hank (the excellent Jack DiFalco), who has never met his aunt, is willing to undergo testing in order to find out. Does he owe something to this woman he’s never met?

Taylor is endearing as a woman who has sacrificed much of her own life to care for her father and aunt, and whose “reward” for it seems so desperately unfair.

I particularly marveled at the way Taylor processed any bad news that comes Bessie’s way. She segues briskly from shock to resilience, with the speed and force of a Gulf Coast storm, the way some people—lucky people—can do when faced with ill circumstances that are beyond their control.

It’s easy, as well, to empathize with Garofalo’s chain-smoking Lee (the smoking, by the way, is the only indication “Marvin’s Room” is set some years ago). Hank’s adolescent meltdowns have already pushed Lee to the brink, even before Bessie’s diagnosis spurred this undesired trip from Ohio to Florida.

Though Lee will be short and snappish with Bessie, she also has clearly arrived with a determination to get back in the ring of family dynamics, and make up for lost time.

Weston (TV’s “Alice”) is here partly as comic relief, but she’s more than that. Ruth has retreated into TV soap operas, but Weston doesn’t let her become a caricature. In fact, her Ruth is something of the family anchor, with humanity on unabashed display the day she decides to get dressed up in celebration of nuptials … on her beloved serial.

Do we not all sometimes prefer the company of our television programs to our loved ones?

The American Airlines Theatre isn’t a particularly forgiving venue for a story quite so intimate, but designer Laura Jellinek succeeds in taming the open space, using a turntable and blocks of colored glass to transport us from Bessie’s home, to her doctor’s office and a key turning point at—why not?—Disney World.

There’s a graceful, late-night exchange between Bessie and her nephew that I think really gets at the core of what McPherson was doing with “Marvin’s Room.” Hank is surveying his surroundings, and Bessie explains there was once a patch of bushes that afforded a view to the Gulf of Mexico, before new construction spoiled the sight.

“You can still smell the water, though,” she tells the boy. “Marvin’s Room” is at its finest when reminding us that memory is a fierce, potent counterpoint to fear of the unknown.

“Marvin’s Room,” through Aug. 27 at the American Airlines Theatre, 227 W. 42nd. St. Tickets: $47-$147. Call 212-719-1300.

Follow Robert Kahn on Twitter@RobertKahn