Rive was born in Cape Town and grew up in the "Coloured" and mixed-race area, District Six. He studied at Hewat Training College, where he also spent a large part of his working life as an English lecturer, and at the University of Cape Town, and then at Columbia University. He completed his doctorate on Olive Schreiner at Magdalen College, Oxford.

He was a champion hurdler in his youth and was active in sport coaching and organisation throughout his life.

In the late 1950s he started writing short stories about the iniquities of the apartheid system and produced his first novel, Emergency, about the Sharpville massacre, in 1963, and an autobiographical Writing Black, in 1981.

His short stories, which were dominated by the ironies and oppression of apartheid and by the degradation of slum life, have been extensively anthologized and translated into more than a dozen languages. He was considered to be one of South Africa's most important short-story writers. While he was one of the prominent black voices of literary protest, he never alluded in his work to his own homosexuality or to gay and lesbian issues.

He was stabbed to death by a pair of "rent boys" in his house in Cape Town, just when an adaptation of his novel "Buckingham Palace", District Six (1986) was being staged to much acclaim at the Baxter Theatre in cape Town, and just after his finishing another novel, Emergency Continued.