Australia need a nine-wicket final session to claim an unlikely clean sweep of South Africa after the Proteas went to tea at 1-46 on the final day of third Test at the SCG.
After South Africa offered firm resistance in the first session on Sunday they were bowled out for 255 after lunch, with Josh Hazlewood wreaking the damage.
That allowed Australia to enforce the follow-on with a 220-run lead, keeping hopes alive of a Test win after close to two days were taken out of the match by rain.
Pat Cummins then removed Dean Elgar before the tea break, with the out-of-form South Africa captain caught behind down the legside for the fourth time in the series.
But the Proteas were otherwise unscathed in the opening 15 overs, with Sarel Erwee and Heinrich Klaasen both not out on 18.
A minimum of 32 overs will be bowled in the final session, with South Africa trailing by 174.
A win for Australia would secure their spot in June's World Test Championship final.
Otherwise, they would need to win or draw one of the four Tests in India next month, or hope New Zealand do not lose both their home Tests to Sri Lanka in March.
Australia could have been far closer to victory if not for missed chances, including three dropped catches in two overs off the bowling of Travis Head.
Head, Marnus Labuschagne, Alex Carey and Ashton Agar missed opportunities in the field in the first innings, potentially harming Australia's chances of winning.
It was Hazlewood who kept them alive.
After Simon Harmer and Keshav Maharaj provided the main resistance in the first session, it was the paceman who claimed their wickets after lunch.
He trapped Maharaj lbw for 53 before bowling Harmer after the right-hander had soaked up 165 balls for his 47.
That left Hazlewood with first-innings figures of 4-48, while Cummins finished with 3-60 after effecting the damage late on day four.
Nathan Lyon and part-time spinner Travis Head also claimed first-innings wickets, while Australia's second specialist spinner Agar went wicketless in his first Test in five years.
