Andrew Haigh’s film takes its title from the Willy Vlautin book from which it was adapted, but also from the name of an over-the-hill quarter horse that is a character in it. The focus, however, is not on the animal, but on a fifteen-year old boy who—in an emotional sense—comes to lean on the horse during a particularly difficult time of his life. The lad, Charley Thompson, is played by Charlie Plummer, and the young actor is the true linchpin of the film, giving a performance of rare insight and dramatic impact.

Charley has just arrived in Portland with his dad Ray (Travis Fimmel); his mother abandoned them years earlier. Ray obviously has great affection for his son, but he’s hardly a responsible father, more interested in shacking up with women like Lynn (Amy Seimetz), a secretary from work who’s separated from her husband, than in caring for the boy.

One day while out running in hopes of making his new school’s track team Charley comes upon a local racetrack where he meets horse owner Del (Steve Buscemi), whom he asks for a job. Del takes the kid on temporarily, and Charley proves such a hard worker that the job becomes permanent. He develops a special attachment to Lean on Pete, a five-year old whose racing days are coming to a close, though jockey Bonnie (Chloe Sevigny) warns him not to. She’s right, because while Del likes the kid, he’s a practical guy, and decides to sell the animal to a Mexican slaughterhouse.

It’s not the only loss Charley is faced with. Lynn’s husband comes after Ray one night, and his father winds up severely injured and hospitalized. What follows leads the boy to a fateful decision: he takes off with Lean on Pete to a journey to Wyoming, where he thinks his Aunt Margy (Alison Elliott) might live. He remembers her as the only person who really showed him kindness after his mother’s departure; but she and Ray became estranged, and hadn’t spoken in years.

The trip is a hard one, portrayed as a depressing picaresque. Charley is desperately short of money, and at one point is threatened with jail when he tries to eat and run at a roadside diner. On one occasion he take a job with a Mexican painting crew, only to have his earnings stolen by hop-head Silver (Steve Zahn), who befriends the boy at a soup kitchen and offers him a bed in his trailer—which prompts Charley to take uncharacteristically violent action. On another he finds temporary refuge with a couple of slacker war vets at an isolated cabin, where he shares a poignant conversation about people who have no choices in life with a girl who visits with her abusive grandfather. By the time he reaches Wyoming, Charley is alone and desperate.

Haigh, who treated a marriage in crisis with delicacy and compassion in “45 Years,” deals with the tragic circumstances young Charley must confront in a similarly humane, empathetic fashion. It’s possible to question some of the casting choices—certainly Buscemi isn’t the first actor you’d think of to play a crusty old western horse owner, though he manages to carry it off, nor is Zahn a natural choice as a scummy thief (and he doesn’t fully convince). But Fimmel, once a handsome hunk, is thoroughly persuasive as a shaggy, run-down womanizer, and Sevigny, another odd choice, brings a touching quality to the spunky jockey who befriends Charley, becoming almost a surrogate aunt to the boy. Under Haigh’s sure hand the rest of the supporting cast etch compelling small portraits, and the technical contributions—from cinematographer Magnus Jonck, production designer Ryan Warren Smith, costumer Julie Carnahan, and editor Jonathan Alberts—are all outstanding, as is James Edward Barker’s understated score.

But it’s Plummer who’s essential to the film’s success. In a performance remarkable for its range, he captures every nuance of Charley’s emotional journey, from his early uncertainty with Ray and Del to his heartbreak in the last act and his tearful reaction to a chance at a better life at the close. The young actor was good as John Paul Getty III in Ridley Scott’s “All the Money in the World,” but here he is truly extraordinary, and he works with Haigh to create as harrowing and unforgettable a portrait of adolescent turmoil as François Truffaut fashioned in “The 400 Blows.” Those who were impressed by the treatment of children on the edge in “The Florida Project” will be equally moved by what Haigh and Plummer have achieved in “Lean on Pete.”