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Small time New Jersey attorney Mike Flaherty (Paul Giamatti), the hero of Win Win, has economic downturn stress. His client load is dwindling. At the modest building that serves as his law office, the furnace has been making mysterious clanging noises, and Mike is often on his knees, plunging the malfunctioning toilet. The high school wrestling team he coaches, without compensation, is hopelessly bad. Meanwhile at home a tree needs to come down, two young daughters require feeding and his sharp-eyed wife Jackie (Amy Ryan) isn't likely to let him forget any of his responsibilities.

None of this sounds like a situation you'd call winning, but it's apparent from the first frames of this edgy but warm film that writer/director Thomas McCarthy (The Visitor) intended the irony. He shows Mike out jogging on a woodsy path, chugging along in his sweats — a plump guy trying — when two sleek runners pass him by and quickly leave him in the dust. Mike stops and huffs and the film's title is stamped onto the screen in giant bold yellow letters. It's the first laugh we have at Mike's expense.

He remains a steadily sympathetic character though, even when he commits the appalling ethical breach that drives the plot. Mike's elderly client Leo (a taciturn but touching Burt Young) is in the early stages of dementia. His ne'er do well daughter hasn't responded to any of the court's correspondence and the state is about to make Leo its ward and put him a rest home, something he can afford but doesn't want. Mike saves the day with an offer to be Leo's guardian, a job that pays $1508 a month. Except that instead of caring for Leo at his home, Mike immediately deposits the old man in the nursing home, shamelessly using his client's dementia to convince him it was the court's decision.

Based on the casting alone, we have little doubt that this "free" money is going to exact its psychic toll on Mike; Giamatti, with his basset hound eyes, has a face built for suffering. But McCarthy's puts the screws to his leading man in an unexpectedly poignant way. Leo's teenaged grandson turns up on the steps of that now abandoned home. Kyle (Alex Shaffer) has a huge bruise on his cheek, a chronically low affect and bleached blonde hair that causes Jackie to dub him Eminem. She's not sure of what to make of Kyle, and neither is Mike, but they let him stay in their basement for a few days, at least until his drug-addicted mother Cindy (Melanie Lynskey) can be found. When it turns out she's in rehab, Kyle's visit is extended.

The less said of Cindy the better — her true nature should be left for viewers to discover on their own — but I must gush about Lynskey, a New Zealand native who got her start opposite Kate Winslet in Heavenly Creatures in 1994. She's never had that big breakthrough moment but she has become one of the most reliably intriguing supporting actresses in film. In 2009 she had small parts in Away We Go, The Informant! and Up in the Air and although I loathed the first and had mixed feelings about the second, she was wonderful in all three. In Win Win she gives a very different kind of performance and is even better.

Shaffer, with his oddly small features and impenetrable flatness in his eyes, is also uncannily well cast. There's something about a low affect that more typically expressive people often find frightening — that blankness of emotion can feel like facing a black hole — and you can understand Jackie's urge to lock Kyle in the basement at night. Is he just a kid in need, or someone too damaged to be trustworthy? There are no givens here, and we work out the answer at the same time as Jackie and Mike. Is the fact that Kyle turns out to have been a star wrestler back in Ohio a little convenient? Yes. So is the sudden addition of Mike's best friend Terry (Bobby Cannavale, who was so good in McCarthy's first film, The Station Agent) to the team's coaching staff. McCarthy uses him for comic relief, particularly during the wrestling sequences. With all that grappling and groping, we need a color commentator to help us understand this lesser known, goofy-looking sport. Through Kyle, who turns it into a clumsy ballet, we begin to see it as a strangely endearing passion for a strangely endearing boy.

McCarthy deliberately keeps the scope of redemption small. He knows people aren't easy to fix — some people do lousy things, some are just lousy for life — and that sometimes humbling oneself is the only way out of a bind. His writing reflects a wariness of human nature but he's not cynical; indeed, the story wraps up with a tenderness that feels true but completely without mush. The irony of the title fades as Win Win wins you over.

• Mary Pols