Unlike the typical movie car chase, which takes place at breakneck speed and usually involves a few spectacular crashes, the one in “Frozen River” dares to be slow and avoids collisions altogether — yet somehow it’s as exciting as the more conventional versions.

That’s just one of the distinctions of the winner of the Grand Jury Prize at this year’s Sundance Film Festival. It’s also visually haunting, beautifully acted and replete with drama despite its focus on subjects that are decidedly unsexy by Hollywood standards.

The central figure is Ray Eddy, a part-time sales clerk who lives with her two sons in the hardscrabble upstate New York town of Massena. Ray struggles daily to feed and shelter the boys after her gambling-addicted husband has decamped with savings that were intended to buy a new double-wide for the family.

Ray is movingly portrayed by Melissa Leo. Working from the spare but fully rounded script by director Courtney Hunt, she builds a character who is palpably desperate, yet determined to protect her sons no matter what it takes.

What it takes is agreeing to smuggle illegal aliens from Canada into the U.S. by driving them across the frozen St. Lawrence River in the trunk of her car.

It’s a dangerous but lucrative sideline that she falls into with the encouragement of a young Mohawk Indian widow named Lila Littlejohn. Like Ray, Lila is desperate, though her need is less financial than a yearning to reclaim the infant son who has been taken by her in-laws.

After an acrimonious beginning — Ray catches Lila swiping the car that belongs to Ray’s missing husband — the women form a grudging relationship that is one-tenth bonding and nine-tenths partnership in crime. As Lila, Misty Upham is more understated than Leo but almost as affecting.

After the deceptively leisurely car chase and other adventures with low-life smugglers, frightened immigrants and stern border patrolmen, the movie closes on a note that is positive but way short of hopeful. These characters will always have to struggle. Massena and the nearby Mohawk reservation will always be bleak. And the St. Lawrence in winter will always be icy and treacherous.