Set 632 to win after the Proteas were finally dismissed for 569 in their second innings on the back of Hashim Amla and AB de Villiers centuries, Australia were 40 without loss at stumps on the third day on Sunday.
The Australians still need a further 592 runs to win with two days to play.
David Warner will resume on Monday's fourth day on 29 with Ed Cowan not out nine.
It was Amla's 18th Test century and he faced 221 balls, hitting 21 boundaries.
After resuming at 99 not out on the third day, Amla took just three balls to reach triple figures, having faced a mere 87 balls.
De Villiers reached his 14th Test century in memorable fashion just before tea, audaciously reverse-sweeping spinner Nathan Lyon for three successive boundaries to reach the milestone.
Left-armer Starc cleaned up the South African tail to claim his first five-wicket haul in Test cricket and finish with six for 154 from 28.5 overs.
The Australians still need a further 592 runs to win with two days to play.
David Warner will resume on Monday's fourth day on 29 with Ed Cowan not out nine.
It was Amla's 18th Test century and he faced 221 balls, hitting 21 boundaries.
After resuming at 99 not out on the third day, Amla took just three balls to reach triple figures, having faced a mere 87 balls.
De Villiers reached his 14th Test century in memorable fashion just before tea, audaciously reverse-sweeping spinner Nathan Lyon for three successive boundaries to reach the milestone.
Left-armer Starc cleaned up the South African tail to claim his first five-wicket haul in Test cricket and finish with six for 154 from 28.5 overs.
