The South Africans need 127 runs off a minimum of 30 overs in the last session for the highest successful fourth-innings run chase.
Faf du Plessis and AB de Villiers shared an unbroken 134-run partnership and batted all through the second session at the Wanderers to take South Africa ever closer.
Du Plessis was 88 not out having batted for nearly four hours since coming in late on Saturday. De Villiers was unbeaten on 72, with the result still surprisingly uncertain heading into the last session.
India were favoured to close out a big win after setting the South Africans a mammoth 458 for victory.