As a low-key exercise in illustrating the scope of human compassion, “The Visitor” is a terrifically well-meaning film whose story is too tidy in its symmetries, though often redeemed by its performances.

Walter Vale (the character actor Richard Jenkins) is dead in the water. He’s a 60-something college professor whose Connecticut home has the emptied-out feeling that usually suggests a soul-sapping loss. Stalled on a new book about global economics and bored by his job, he spends lonely nights trying to master the piano, and stirring pots of canned spaghetti sauce. Gradually, we sort out that his wife, a classical pianist, died some years before, and that Vale has never escaped his grieving funk.

Dispatched to Manhattan for an academic conference he’d rather avoid, Vale digs out the keys to an apartment he’s kept in the city. Gingerly revisiting an earlier life, he quickly discovers that he’s got company. An immigrant couple, the Syrian Tarek (Haaz Sleiman) and his Senegalese girlfriend Zainab (Danai Gurira), have taken residence, apparently given access by an unscrupulous superintendent. Confusion abounds, but after the shock wears off, the pair leaves, only to return when Vale offers to host them for a spell, unexpectedly moved by a photograph they’ve left behind: a romantic image of radiant lovers, sharing a bond that Vale hasn’t experienced in a long, long time.

Director Tom McCarthy’s follow-up to his Sundance favorite, “The Station Agent,” once again congregates mismatched souls on the path to quirky epiphany. Vale may not be much at the ivories, but when he catches Tarek practicing on the djembe — the single-headed, goblet-shaped hand drum from West Africa — he becomes fascinated with the polyrhythms. Soon enough, he’s taking lessons from Tarek and jamming along in Central Park drum circles, an old white guy in a lawyer suit, getting down with the dreadlocked dudes and the old-school congueros.

Up to this point, “The Visitor” is mild-mannered midlife crisis fare embellished with neat little ironies. It’s Vale, of course, who is a stranger in his own life — not his guests from the Third World, who are as earthy and vibrant as he is pallid and diffident. The academic is presented as an expert on the economies of developing nations, but only now is learning about Nigerian Afro-Beat after Tarek hips him to Fela Kuti.

The cultural codes are distressingly prefabricated, though to their credit, the actors strive for depth. Mr. Jenkins, especially, plumbs the screenplay’s poignant silences for the broken pieces of his character’s life. Then the story takes a sharp turn. Tarek is arrested after a misunderstanding in the subway and taken to a detention center for illegal immigrants in Queens.

Suddenly flush with purpose, Vale invests himself in the cause, hiring a lawyer and making trips to the grim facility to visit Tarek, who, it seems, had been refused political asylum years earlier. Unfortunately, the tone of the film gets hijacked by this post-September 11, Middle-Eastern immigrant persecution theme, which jostles uneasily with the subtle chemistries between the characters. The arrival of Tarek’s mother (the wonderful Arab-Israeli actress Hiam Abbass) fails to resolve the issue, but it does provide occasion for a gently observed courtship. Mr. Jenkins, who played a cranky ghost on several memorable episodes of the HBO series “Six Feet Under,” allows his character to flicker back to emotional life in ways that feel earned and true, unlike the film’s bumper-sticker sentiments on social injustice, which are more shrill than shrewd.