Jane Campion's latest film is not really a western, but if it were it would be one of those that – among other business – marks the final shift from residual frontier to something like civilisation. Set in rural Montana during the mid 1920s, this adaptation of an underappreciated Thomas Savage novel hangs around the clash between two different brothers. Despite an apparently expansive education, the bitter, sexually-repressed Phil Burbank (Benedict Cumberbatch), whose every word is salt on sensitive skin, revels in the toil and filth of a cattleman's lifestyle. "I stink, and I like it," he barks after a day's work. George Burbank (Jesse Plemons), his gentle, less colourful sibling, dresses in sensible suits and speaks in the language of a mid-century businessman. If he lives long enough he will enjoy dozing off in front of I Love Lucy.

The tense equilibrium is such that, despite inhabiting something like a mansion, the two men share a bedroom reasonably comfortably until George marries Rose (Kirsten Dunst), the widowed keeper of a nearby saloon. When she and her deceptively fragile son Peter (Kodi Smit-McPhee) move on to the ranch, a psycho-drama kicks off that will leave all four players rubbed raw. Only comfortable out on the plains where no man or woman can inhibit his venomous ego, Phil patronises George, bullies Peter and aggravates Rose’s developing alcoholism.

It would be wrong to overwork arguments about alienation in the face of advancing civilisation, but Phil does offer a surprising variation on the archetypal last cowboy. He is fiercely intelligent. He is quietly cultured. One of his most insidious tortures finds him upstaging Rose’s awkward piano rendition of the Radetzky March with a more dextrous version on the banjo. This irredeemable thug could have been a monster in any environment.

To say that Campion makes the most of this horrible quadrilateral dispute would be to understate the case. The Power of the Dog is certainly her most gripping film since The Piano and possibly her most impressive since An Angel at My Table in 1990. Always strong with actors, she teases an impressive cast towards their best work yet. Plemons makes the case for steady acquiescence as a worthy character trait. Dunst subtly deliquesces from shyness to dipsomaniac oblivion without going over any obvious psychological edge.

If the drama has a flaw it is that those two compelling characters complete their journeys relatively early and leave the remainder to Phil and Peter. The film's title is from the Bible and their ruinous rivalry is worthy of an Old Testament melodrama. Cumberbatch has, over the last decade, too often played similar incarnations of a likeable neurotic – Holmes, Strange, Turing – but the diminishing returns are here reversed with a personality who, though troubled enough to deserve a syndrome in his own name, emerges as fully fleshed as a character from George Eliot. Cumberbatch's greatest achievement is to inject just a modicum of pathos into a man who lives to batter others with his own unprocessed misery. Smit-McPhee holds his own in the whirlwind with a performance that begins with concealment and ends with startling (if unshowy) revelation.

The cinematic machinery around the drama is of the highest quality. Jonny Greenwood delivers an anxious, often pizzicato score that inevitably points up wider reminders of There Will be Blood. Residents of the American west must decide if Campion's native New Zealand – shot on yawning widescreen by Ari Wegner – is convincing stand-in for Montana, but, to these European eyes, it plays like a nightmare vision of Big Sky Country. Working halfway round the world, Campion has fashioned a startling translation of later chapters in the American creation myth.

Wide-open spaces have never seemed so claustrophobic.

Released in selected cinemas on November 19th and on Netflix from December 1st