When Young Fathers’ debut album, Dead, won this year’s Mercury prize, it was surprising largely because the record initially appeared so inaccessible. Its brooding, murky air of menace is intermittently immersive, though so eclectic and nebulous that it is virtually impossible to pin down.

Live, the Edinburgh hip-hop trio render such reservations irrelevant by being thrillingly visceral and in-your-face. Alloysious Massaquoi – born in Liberia – Kayus Bankole, whose parents are Nigerian, and Scottish Graham “G” Hastings all bring disparate influences to the table, but as a fluid performing unit they generate a synchronised anarchy that is frequently jaw-dropping.

Their staccato, screwed sonic mosaics unfold over the kind of military yet frenetic, stiff-armed drumming more usually associated with Laibach. Yet the three vocalists appear on the verge of coming to blows as they wrestle over the mic to spit out the agitated, jittery rhetoric of the seemingly mock-jihadist No Way: “AK-47 take my brethren straight to heaven.”

Their lyrical manifesto is opaque and elliptical but delivered with a ferocious intensity. Bankole is a pogoing, jackknifing human dynamo on the personal-is-political rallying calls of Queen Is Dead and Just Another Bullet. When collaborator and support act Lauren Holt, AKA Law, joins them for the second half of their set, she is a sublimely serene and aloof counterpoint to their inchoate rage.

The taut, righteous party anthem Get Up is all serrated slogans and rhythmic detonations, like some unholy 21st-century marriage of James Brown and Public Enemy, and a fantastic set climaxes with a white-noise freakout, a devastated drum kit and ecstatic tribal chanting. Forget the Mercury: on this astounding evidence, Young Fathers deserve to win every prize going.

• At Edinburgh’s Hogmanay Street Party, 31 December. Box office: 0844 573 8455.