She doesn’t sing. Her speaking voice isn’t an exact match. Her wig’s a bit off, and her eyebrows aren’t bold enough.

Yet for the 90 minutes she was onstage, I was quite willing to go along with the idea that Adrienne Barbeau was Judy Garland.

It can’t be easy to compete with the small army of Judy Garland impersonators – that phalanx of mostly men in drag who are dead ringers for the late singer-actress. Ms. Barbeau, wisely, declines to go for spot-on mimicry. She gives Garland just enough of the familiar packaging to establish the resemblance, then backs off the fussy trappings. Instead, she focuses on Garland’s most unforgettable quality – her arresting, piteous vulnerability.

“The Property Known as Garland,” now playing at the Actors’ Playhouse, is set backstage at Garland’s final concert in Copenhagen in March 1969. Three months later, her fifth husband, Mickey Deans, found Garland dead at 47 in her bathroom; the cause was an overdose of barbiturates.This is essentially a one-woman show (with a bit player who comes backstage and tells Ms. Garland how long until curtain). As such it has two chief ingredients: its script and its star.

The script, by Billy Van Zandt, has some good, breezy raconteur bits, but it also falls into the trap of too much forced explication. There are some laugh-out-loud punch-lines, but also some real clunkers. Mr.Van Zandt has a tendency to reach too hard for the show-biz insider quip, and his fondness for the big cliches (e.g. Judy only feels alive onstage) too often gets the best of him. Worse, the disembodied voices of Garland’s mother and Louis B. Mayer speak to Judy periodically in flat, pre-recorded bursts that seem amateurish.

But then there’s the star. And somehow Ms. Barbeau sails through it all, sweeping us along with her. Her ability to play up the wheat while glossing over the chaff is quite remarkable. She emerges as – if not the Judy Garland – a plausible version of Judy Garland, one with warmth to offset the brittleness, wit to offset the hard knocks.

Few people probably expected such a performance from Ms. Barbeau, who has not been on the New York stage since she played Rizzo in the original “Grease” more than 30 years ago. Since then, she has been a busty B-movie queen, a pinup girl, and primarily a television actress. Likely no one would have considered her for the part of Garland,were it not for the fact that Mr. Van Zandt, who wrote “The Property Known as Garland,” is her husband.

Even so, Ms. Barbeau initially balked, worried about the complexity of portraying such a well-known person. But perhaps Ms. Barbeau, whose significant show-biz ups and downs are chronicled in a forthcoming memoir called “There Are Worse Things I Could Do,” can relate to a woman who was chewed up and spit out by Hollywood several times, reinventing herself after every setback.

The show’s tone is far more bittersweet reflection than edge-of-the-abyss raving, and the heroine of “The Property Known as Garland” is a gentle soul who was a victim of circumstance.

So this Judy Garland is a softie. Even when she’s acting like a capricious diva, threatening to cancel the show if she doesn’t get some mashed potatoes, there’s no chill in it. She remains self-aware; laughing at her own actressy temperament all the while. This, of course, is a bit of a lie; the desperate audiotapes Garland made near the end of her life suggest the strength of the demons that haunted her. But it’s hard to expect anything else from this love letter. This is a Judy Garland play for people who take comfort from hearing “Over the Rainbow.”

Whatever liberties it takes, “The Property Known as Garland” has enough of Garland’s fascinating personal history to keep you involved. (It’s one of the great show-biz tragedies, with a stage mother and a vile, totalitarian studio and a girl irresistibly drawn to the power her voice had over adoring fans.) Glenn Casale’s minimalist direction keeps the focus on Ms. Barbeau. And she draws you in, creating an attachment to this bruised loner who, after being so profoundly damaged, can still joke and laugh and dream. “The Property Known as Garland” may not be a memorable show, but Ms. Barbeau’s is a memorable performance.

Until June 4 (100 Seventh Avenue South at Grove Street, 212-239-6200).