Invictus takes its title from a poem by Britain’s William Ernest Henley, first published in 1875, that Nelson Mandela recited while imprisoned on Robben Island for 18 of his 27 years in captivity. It is Latin for “unconquered,” an apt summation of Clint Eastwood’s workmanlike drama about the power of sport to promote unity in post-apartheid South Africa.

The movie belongs to that timeless genre, the stories of underdogs inspired to greatness and guided to victory on the strength of desire. How else to explain the improbable triumph of the Springboks, the nation’s underachieving rugby team and a longtime symbol of white-supremacist rule? They are, as one spectator puts it, a disgrace – sloppy on the field and resigned to mediocrity.

Mandela sees them as a means to an end: Embraced by the country’s white minority but derided by blacks as a link to the repressive past, the Springboks are uniquely positioned to rewrite their legacy, to facilitate change in a nation bitterly divided. The year is 1995, and the Rugby World Cup is coming to Johannesburg. Mandela believes a win there will be a small but important step in the healing process. But how to achieve it?

He meets with Francois Pienaar (Matt Damon), the fair-haired Springboks captain who, Mandela’s daughter tells him, looks like an old-guard policeman. Pienaar is an easy ally – he recognizes the import of the moment – and the matter is resolved. The Springboks will win the Cup for South Africa, whose grateful citizens will put aside their differences and cheer the team on as one.

Wisely, Eastwood devotes little time to game action until the championship, in which the Springboks, seemingly outclassed by New Zealand’s All Blacks (named for the color of their uniforms, not their racial composition), scrape their way into the history books with Mandela watching over them like a proud parent. It’s a rousing win for team and country.

Anthony Peckham’s script, adapted from John Carlin’s exhaustively detailed account of the game and its impact, rarely scratches beneath the surface – Mandela is a benevolent sage and Pienaar his willing accomplice, but they reveal little about themselves otherwise. Their story unfolds neatly – perhaps too neatly – with a soundtrack that’s wanting for subtlety, yet this is a worthy addition to Eastwood’s resume.

For that, he can thank the Springboks, whose victory amounted to a real-life fairy tale, and his stars, who rise to the occasion with equal vigor. Damon, who gained 30 pounds of flab for The Informant! but added plenty of muscle for Invictus, is convincing as the team’s strong, mostly silent field general. Morgan Freeman, whom Mandela once described as the actor best suited to play him, provides a presence as warm and reassuring as the former president’s own.

Some have criticized Eastwood for playing it safe, casting a bankable white star opposite Freeman in a movie that aspires to tell Mandela’s story. The argument is dubious at best: Invictus belongs to neither Mandela nor Pienaar, but depicts an instance in which the president reached out to an apolitical Afrikaner in hopes of achieving a goal bigger than both of them.

Give Eastwood his due. He has taken a story that deals with racism and rugby – not exactly box-office draws – and worked within a studio system that favors remakes and sequels to get his movie made. For that, respect must be paid.