No actor has mastered the art of muttering obscenities under his breath more expertly than Dennis Farina. In “Get Shorty,” “Snatch” and other films about low-life criminals, Farina, with his eagle-eyed glare, Charles Bronson-like mustache and clenched-teeth diction, has stolen every scene he’s in merely by spouting off an array of expletives. “The fucking airport,” he barks at a cab driver in “Get Shorty,” disgusted at being put upon to give simple directions. His every eyebrow twitch, stiff-necked shrug and sarcastic overemphasis on every word—as if he’s already explained what he’s saying three times—deliver the message: “I don’t give an inch for you—you give an inch for me.”

Happily, Farina’s signature macho style is put to good use for much of “The Last Rites of Joe May.” But the film, directed and written by Joe Maggio, stretches Farina’s range to an unexpected level: for the first time, he’s showing genuine hurt and weakness, with astonishingly powerful results. Joe May certainly bears the same hostility and bitterness as Farina’s other characters, but he’s a man with a conscience, a soul, and his brooding takes on a tragic dimension.

The film begins with Joe, an aging, low-level street hustler, leaving a two-month hospital stint. Still crippled by pneumonia, he skulks back into his dreary Chicago neighborhood, only to discover that his landlord threw all his belongings out and rented his apartment to a young hospital worker (Jamie Anne Allman) and her daughter (Meredith Droeger). Homeless, his vehicle impounded, his bank account nearly empty, he’s reduced to wandering through icy, darkened streets and nodding off on buses. Spotting him huddled beneath his beige leather jacket one night, Allman takes pity on him and invites him to share the apartment.

The “last rites” of the title refer, naturally, to Joe’s redemption, developed through his budding relationship with, and sense of duty to, Allman and Droeger.

Thematically the film is distressingly familiar: a fallen-soul-finds-peace story in the vein of “The Wrestler,” “Crazy Heart” and “Affliction.” The lighting is punishingly dim, meant to mirror the bleak proceedings but often just making the picture tough to look at. And some of the characters, while necessary to keep the plot in motion, are ciphers through and through: Joe’s estranged, angry son (Brian Boland), the battered single mom (Allman), the abusive boyfriend/corrupt cop who’s “under a lot of pressure” (Ian Barford).

Maggio throws in plenty of “Wrestler”-like sentimentality, as we watch Joe sink deeper into despair. A one-time pro at hawking watches and electronics, Joe is now mocked by his shady employer (Gary Cole, effectively smarmy), assigned demeaning tasks like selling lamb meat to unfriendly grocers. Besides the sweet little girl (played nicely by Droeger, who is a refreshingly low-key child actress), Joe’s only true friends are his pigeons, which he houses in a coop on his roof. As if the main story wasn’t dramatic enough, Maggio torpedoes key scenes with excerpts from Puccini’s “La Boheme” and Verdi’s “Trovatore.” Countless films, from “Moonstruck” to “Philadelphia,” have used opera to underscore human frailty but never as shamelessly as here.

Yet despite the film’s flaws, Maggio does achieve several dark comic moments to break up the lingering aura of gloom. There’s a painfully funny sequence where Joe loses the fifty-pound cut of lamb to a feral dog, after trying in vain to sell it. The exchange between Joe and the snooty DMV clerk (Jack Bronis) when he tries to retrieve his car is a hoot (“I don’t know the blue-book value on an ’89 Cutlass, but I think you’re getting away with murder,” he says, after telling him the DMV sold the car for $400).

But mainly, “The Last Rites of Joe May” will be remembered as a tour de force for Dennis Farina. Watching him weep over the loss of his pigeons, or run pathetically from the psycho cop, is to witness a celebrated character actor’s ascent into multi-faceted, Oscar-worthy territory. Farina will always be at his best when exhibiting futile rage (“I pray you hit a lamp-post, you fucking hump!” he shouts, hilariously, at an unhelpful cab driver). But “The Last Rites of Joe May” allows his softer, more vulnerable side to come through, and it’s intoxicating to behold.