In the new production of Jen Silverman’s “The Roommate,” one of the two sole characters, introduced as Robyn, makes her entrance clad entirely in black, her eyes concealed behind dark sunglasses. The other, Sharon, turns up in softer, lighter shades, from her plaid shirt to her blond braids.

The latter, a lifelong Midwesterner who comes across as goofily, almost preternaturally wholesome, is portrayed by Mia Farrow, whose delicate, angelic beauty began captivating TV and film fans — and an eclectic assortment of famous men — six decades ago. Yet it turns out that Sharon, who marks the actress’s first role on Broadway in a decade, is no angel.

Robyn is played by a three-time Tony Award winner, Patti LuPone, who made waves in theater circles two years ago by announcing that she was giving up her Equity card, contending that the union did not “support actors at all.” Happily, the same cannot be said for this play, or for its celebrated director, Jack O’Brien — the owner of six Tonys, including a special honor for lifetime achievement — who expertly guides the veteran actresses in this staging.

Sharon and Robyn are women of a certain age; the script identifies them as “50s-70s,” though Sharon admits to being 65, and the spry, attractive Mses. LuPone and Farrow are 75 and 79, respectively. Aside from that, the two would appear to have little in common: Sharon, an Illinois native who lives quietly in Iowa — the states are “quite different,” she insists — describes herself as retired from marriage, and her social engagement is limited to a book club.

Robyn, who has answered Sharon’s ad for a roommate, is a lesbian from the Bronx, whose vegan diet includes regular servings of home-grown marijuana. She has juggled a variety of creative pursuits, from pottery to slam poetry; but when Sharon, who admits to being “very nosy and very persistent,” presses her for more details about her work and personal life, she’s distinctly evasive.

If the ensuing action follows not unfamiliar formulas — opposites become confidantes and comrades, golden girls make mischief — the playwright, whose various credits include “Collective Rage: A Play in 5 Betties” and Netflix’s “Tales of the City,” traces the bond forged between the characters with a piquant wit and gentle, compelling insights. Both are beautifully served by the players under Mr. O’Brien’s sharp but compassionate direction.

Ms. LuPone disclosed in a recent interview that Annette Bening was initially sought for the part of Robyn, and I’m sure that Ms. Bening, given her sturdy intelligence and her flair for dry humor, would have done a bang-up job. But Ms. LuPone brings an underlying warmth to the role that pokes through even when Robyn is at her most terse and cutting — and, predictably, she’s hilarious in those moments as well.

As for Ms. Farrow, it’s hard to imagine a better vehicle for the deceptively fragile-looking star than the long-repressed, superficially flighty, and very funny Sharon, who from the beginning tries in vain to hide how surprised and titillated she is by Robyn’s revelations. “I kissed a girl once in college,” Sharon notes, upon learning of her new roommate’s sexual orientation; the next scene opens with Sharon on the phone, breathlessly telling her son, “She’s a homosexual!”

Sharon develops her own infatuation with Robyn as the play progresses, but the attraction, and the genuine love that grows between them, aren’t of an erotic nature — at least, not primarily. “You have to stop thinking about yourself as basically dead,” Robyn tells her, relatively early in their relationship; only after learning some truly ugly secrets about her guest’s past does Sharon begin to feel, in her own words, “smarter and faster and younger than I knew I could be.”

If Sharon’s journey provides some delightful dark comedy, it is also marked with pathos, and Ms. Farrow is radiant in traversing both aspects. “There’s a great liberty in being bad,” her Sharon resolves at the end, repeating verbatim a line first spoken by Ms. LuPone’s Robyn. In truth, both characters learn from, and are to some extent liberated by, each other, and both stars make that education buoyantly entertaining.