South Africa need 69 runs to win in their second innings, with eight wickets in hand, to win the world title.
Opening batter Aiden Markram and captain Temba Bavuma kept South Africa in contention on Friday, sharing an unbroken partnership to carry the match into day four in the World Test Championship final against Australia in London.
Returning to the crease for their second innings at the start of the afternoon session on day three, South Africa were set a target of 282 runs to win.
At the close of play, they had reached 213/2, still needing 69 runs to secure the global title with eight wickets in hand and two days remaining.
Markram was on 102 not out and Bavuma, who was struggling with a left hamstring strain, was unbeaten on 65 when stumps were drawn.
Australia second innings
Earlier, in the morning session, Australia resumed their second innings at 144/8, and tail-ender Micthell Starc stuck his heels in, carrying his team to 207 all out.
Starc was persistent, hitting 58 not out off 136 balls – his 11th Test after spending more than three hours at the crease – but he ran out of partners at the lunch break.
Fast bowler Kagiso Rabada, who bagged five wickets in Australia’s first innings, took 4/59 to return match figures of 9/110.
He was well supported by seamer Lungi Ngidi who took 3/38 after going wicketless in the first innings of the match.