It’s a trick he’s performed before with 9/11 plane hi-jacking drama United 93, but Captain Phillips might just be his best work yet. And it’s certainly Tom Hanks’ best performance in a very long time. Both can likely prepare for a glut of awards.

Captain Phillips is based on the true story of the Maersk Alabama, a cargo ship that runs afoul of Somali pirates off the coast of East Africa, and the ship’s captain – here played as a believable everyman by Hanks – who does his best to protect his cargo and his crew, and later finds himself held for ransom in the close quarters of a tiny life-boat.

Greengrass’ naturalistic style and documentary roots make him the perfect auteur for this story. Where it would be easy to turn a tale like this into a sea-faring Die Hard, Greengrass ensures everything is subtle and authentic. The docks and the ship are both wholly believable, with all the minutiae and machinery of the setting creating a genuinely convincing world. Everything is distinctly unflashy; the cast are unknowns and non-professionals, while the action is entirely plausible.

The cat & mouse game that ensues on the ship is superb; these are sequences as tense and suspenseful as any you’ll see all year, while the initial pirate incursion is riveting.

Midway through, the canvas both widens and contracts. Suddenly, rather than just pirates and the crew, there are Navy warships and SEALs on the scene – but while the rest of the world takes notice, most of the action shifts to a tiny, claustrophobic hot-box of a life-boat. And if you thought the first half was tense, the close quarters only make it more unbearable, and the soundtrack that pulsates throughout will leave you breathless.

Tom Hanks hasn’t been this good in a very long time. You might think that as the big Hollywood man among all the non-professionals that Hanks would stick out like a sore thumb, but his performance is so rich and well judged that he blends in perfectly.

Hanks plays Phillips as an everyman; that is to say that it’s not always the most flattering role. Phillips is a good captain, but his dealings with the crew single him out as a hard man to get along with, and there are moments when he does not come off in a good light. And despite Phillips’ many heroic actions when the danger arrives, he’s never an action hero; simply a man doing what he can.

By the end, when the weight of Phillips’ experience finally catches up with him, it’s heart-rending, and Hanks sells it so absolutely that you’ll forget you’re even watching a performance. It’s incredibly powerful and it’s a moment that will stick in the mind for a long time afterwards; Hanks’ work towards the end is simply phenomenal.

But it’s not just Hanks that stands out. Enter Barkhad Abdi as Muse, the leader of the four Somali pirates. Abdi has not acted before, but you’d never know it from this. Greengrass is wise enough to not demonise his pirates, and Muse gets as much focus throughout the film as Hanks does, from the parallel and wildly different departures from wildly different ports to the pair’s attempts to get out of their situation without bloodshed.

Abdi is brilliant, and always keeps his character humanised and somewhat sympathetic, despite his actions. As the film goes on, it becomes ever clearer that Muse is just as trapped – just as much a prisoner in this misadventure – as Phillips is, and as a double-act of men at odds the pair are fantastically, dynamically watchable.

The most terrifying thing about Captain Phillips is that it’s all true. Not just “based on a true story”, but nearly every beat and scene that happens in the film is something that genuinely happened in real life. You might as well be watching a documentary. And as the might of capitalism and the first world – represented by the great, gargantuan Maersk Alabama – strays into the third world, it takes only four men in a tiny skiff to bring the leviathan to a halt.

Greengrass doesn’t shy away from discussing the wider issues that led to the situation, but he never resorts to preaching, or – crucially – judging. Instead what we have in Captain Phillips is perhaps the most authentic action/thriller ever produced, headlined by two incredible performances from two people with very different backgrounds. Much like their characters, both deserve recognition.

Released in UK cinemas on Friday 18 October 2013.