In the most recent Hunger Games movie, Mockingjay – Part 1, an oppressed community marches towards a hydroelectric dam controlled by their nation's dictator. They solemnly sing a song of defiance and charge towards armed soldiers, using weight of numbers to overrun their oppressors. It is a deliberately stirring act forgotten in seconds because the people are little more than sacrificial pawns and the digital effects used bestow no moral weight.

I'm reminded of it only because in the new historical drama Selma, a compelling film about the 1960s American civil rights movement director Ava DuVernay shows the true power of protest and the horrible reality of defying what is institutionally wrong. When her African-American protesters – demanding no more than equality – attempt to cross a bridge and enter the titular Alabama city, they are met with teargas and batons before mounted police ride them down.

You feel every blow – physical and verbal – in Selma, a film that unfolds in the moment and refuses to allow for the stately recreation of the usual historic epic. The movie captures the desire for change and an acceptance of the risks involved, and the characters are never mere outlines illuminating a textbook. There are impassioned speeches but they're matched by seemingly simple gestures, such as protestors linking arms before a non-violent protest gets a violent response, that are woven into an arresting dynamic.

Selma begins with the Rev Dr Martin Luther King jnr (David Oyelowo), the Baptist minister who became the leader of the fight for civil rights, speaking aloud, but his rhythm is off and one of the great orators of the 20th century sounds uncertain. He's in a hotel room, struggling with his tie, and his audience consists solely of his wife, Coretta (Carmen Ejogo). Dr King may be about to receive the 1964 Nobel Peace Prize, but his public triumph is matched to personal doubts.

Written by Paul Webb, and then rewritten by an uncredited DuVernay, Selma finds the essence of Dr King not just in his words from the pulpit and complex interaction with America's then President, the wily Texan Lyndon B. Johnson (Tom Wilkinson), but in the domestic reality of his own home.

One of the film's many achievements is to present Coretta King as a complex character, not just the supportive wife of a Great Man. She offers advice, forcefully meets with her temporarily incarcerated husband's radical rival, Malcolm X (Nigel Thatch), and wears the weight of her husband's decisions. Coretta laments "the constant closeness of death", foreshadowing her husband's eventual assassination in 1968, even while forcing him to acknowledge his infidelity.

Men who have a national holiday in America and a famous U2 song to their name usually get biopics that compress their lives, but Selma pulses with the camaraderie of the Southern Christian Leadership Conference and the faith of the ordinary people, including Oprah Winfrey's Annie Lee Cooper, who essentially go into battle – and in several cases die – for Dr King. It has an evocative, communal energy.

The 1965 Voting Rights Act had given African-Americas the right to vote, but southern states such as Alabama, led by Governor George Wallace (Tim Roth), simply refused to add blacks to the voting rolls. Johnson, who cajoles and threatens with equal ease, wanted to focus on poverty, but Dr King refuses to wait, forcing a confrontation that will end badly so as to gain the necessary media coverage to force change.

Oyelowo burnishes his portrayal with quiet humour and grace, but it's always under exhibited under harsh pressure. Selma doesn't depict his adversaries as hysterical racists but as people from whom superiority via discrimination is a given. When the 500 or so protestors begin their march towards Selma, white residents simply stare at them, as if they're a curiosity to shortly be squashed.

In the cause of winning some prestigious awards, Selma has been tarred with claims of historical inaccuracy, yet no film based on true events is ever an exact reproduction – that's impossible. What Selma does, as it should, is sum up the events and what they represent. Perhaps what bothered some of the film's critics was that an African-American filmmaker had no time for white saviours.

DuVernay, with just her third feature film, knows how to marshal the moments that will become history, making her own iconic images. When the marchers fatefully approach the nondescript Edmund Pettus Bridge, named for a former politician who was also a Ku Klux Klan leader, DuVernay's camera calmly picks out the bridge's sign: the rust on it looks like bloodstains. Selma is where history, finally, is written by the victors.