Lorraine Hansberry is renowned for her 1959 classic A Raisin in the Sun, but she herself considered her final play, Les Blancs, unfinished when she died of cancer aged 34 in 1965, to be her most important work.

After paying extensive dramaturgical attention to various drafts, the brilliant South African director Yaël Farber (Mies Julie, The Crucible at the Old Vic) has unleashed its tragic power, too; a visiting journalist and a returning native son arrive simultaneously in an unnamed African colony as the country is on the tipping point of revolution and acts of terrorism besiege the Christian mission hospital.

The doctors are doing their best, the colonials are trying to maintain stability in the country they love, mistakenly thinking that a benign despotism is the way forward. One radical, shades of Steve Biko, has died in custody under "interrogation."

Hansberry was stirred as a playwright by the great "black" trilogy of the criminal poet Jean Genet in the 1950s, notably The Blacks, in which black actors played whites in order to re-enact a crime. But whereas Genet's playful, absurdist approach dealt with transgressive ideas of racism and sexuality, Hansberry drills down to a more ordinary, "real experience"; Danny Sapani's powerfully conflicted Tshembe Matoseh, the returning prodigal, is ambivalent about the insurgency partly because of what he's seen abroad, especially in Europe.

The play is continuously surprising, wrong-footing an audience just when they think they know where they are with it. So hypnotised were they by the end of the first night that they stood and applauded not just the play but, you could deduce, an act of terrorism and arson. A Genetesque response to this might be: were the whites feeling needlessly guilty, or the blacks gloatingly vengeful? Was this really about our own race relations?

Farber and designer Soutra Gilmour lay down a panoramic, beautiful scenography of sadness. The mission hospital rotates on a central drum while the cast occupies a surrounding landscape in sculptural arrangements. There's a group of matriarchal singers (one of them with a smear of white face paint) playing mournfully at the side and the wordless figure of Sheila Atim as The Woman – the spirit of Africa? – gliding purposefully, mysteriously, through the action.

Sapani's Tshembe is caught in a crossfire of family loyalties, political expectation and the immediate crisis. By all accounts, even James Earl Jones in the brief 1970 Broadway appearance of the play was unable to pull it all together. Although some of the arguments still remain unclear, Sapani provides a centrifugal force of feeling that irradiates the whole evening.

And there are fine, alert contributions from Elliot Cowan as the American journalist, Anna Madeley as the fraught and pressurised doctor who befriends him, ruffled James Fleet as another doctor, a sort of Chekhovian raisonneur, glorious Siân Phillips as the surviving spirit of the mission, razor-edged Gary Beadle as one of Tshembe's brothers, and a wonderfully dyspeptic Clive Francis as the British major who came here to make this country into something; it's not an outpost of empire, but his home…then he shoots someone.

Les Blancs runs at the National Theatre until 2 June.