Australia need a 14-wicket final day to defy Sydney's poor weather and claim a 3-0 series sweep of South Africa after Pat Cummins breathed life back into the rain-soaked Test.
South Africa went to stumps on day four at 6-149 and needing 127 more runs to avoid the follow-on, after Australia declared at 4-475 with Usman Khawaja unbeaten on 195.
It came after the first half of the day was washed away by rain and leaky covers, adding to the loss of all of day three and another 57 overs across the opening two days.
Australia must win the match to wrap up a spot in June's World Test Championship final, taking qualification out of the equation before next month's four-Test tour of India.
The first task will be to dismiss South Africa for 275 or less in their first innings, allowing the hosts to enforce the follow-on and push for the win.
"I think (we can do it)," Josh Hazlewood said.
"From what we saw today we bowled 50-odd overs and took six wickets.
"And the wicket after a bit of traffic down it looked quite nice with Gazza (Nathan Lyon) bowling into that rough."
Hazlewood said himself and Cummins would be able to bowl extended overs without workload concerns with a month until Australia's next Test.
Cummins claimed 3-29 on Saturday, as he bowled with fury in fading light late after he earlier had Heinrich Klaasen caught behind before tea.
The quick set up Khaya Zondo when he bounced him from around the wicket late in the day with a field set for short bowling, before he followed up with a yorker and trapped him lbw for 39.
Zondo claimed afterwards the lbw should have been overturned, as he suggested he hit the ball while also indicating players should have been taken off for bad light.
"There was a spike (on real-time snicko)," Zondo said.
"It was just dark. That's what I felt, it was quite dark. He's not slow is he?
"But we've got a day to bat. We've done it before so I am sure we will be able to do it tomorrow."
The in-form Kyle Verreynne also fell to Australia's captain on 19, edging Cummins to slip after he and Zondo had led a brief fightback for the Proteas with free-flowing strokeplay.
But with Verreynne's exit, the tail is exposed to start the final day.
Hazlewood also bagged two wickets in Australia's charge, as he extended South Africa captain Dean Elgar's woes with a well-placed bouncer that caught the opener's glove on 15.
Elgar had earlier survived an appeal for a diving Steve Smith catch in the slips, with third umpire Richard Kettleborough deeming the ball brushed the grass.
Temba Bavuma was Hazlewood's other victim, caught behind when he hung his bat outside off stump to a seaming delivery and offered his outside edge.
Lyon also outsmarted Sarel Erwee to claim the opener's wicket earlier in the day, with a ball that went straight on and brushed the leaving left-hander's off stump to help start the rot.