The chances of them pulling off the feat looked remote at best as they reached stumps on 77 for four, still 353 runs short of their target.
Nathan Lyon's off-spin did most of the damage as he took two wickets for 15 runs, removing Hashim Amla for 17 and Jacques Rudolph for three.
Openers Alviro Petersen (24) and Graeme Smith (nought) also fell, after the hosts had declared on 267 for eight midway through the fourth afternoon following 54 from Mike Hussey, to leave South Africa with the toughest of asks on the final day.
The tourists' chase suffered an early blow. It was just the sixth ball of the innings when a static Smith edged Ben Hilfenhaus through to Ricky Ponting at second slip for a duck.
Petersen and Amla briefly made life look easy in a second-wicket partnership of 33, sending the ball to the boundary with style and regularity.
But it proved to be short lived as Amla nicked one in Lyon's second over and Michael Clarke just about held on at slip.
It could have been worse for the Proteas, but Jacques Rudolph survived the closest of lbw appeals, referred by Australia, two balls later.
Rudolph's reprieve was short-lived, though, as he was caught at short leg by Ed Cowan off another Lyon delivery.
And South Africa slipped to 45 for four when Peter Siddle bowled Petersen off his inside edge.
AB de Villiers, with a painstaking 12 not out from 101 balls, and Faf du Plessis, who was unbeaten on 19 from 74, avoided further loss before the close, but their task looked a forlorn one.
Remarkably after scoring 482 runs on day one, Australia were under pressure this morning having lost five for 26 last night to resume the day on 111 for five. They knew a good morning for the South Africans could leave the tourists with serious hopes of victory.
Accordingly, and unusually for this all-action Test, Hussey and first-innings double centurion Clarke dug in first thing to see off the early danger.
The pair announced their intentions to up the rate with a driven four apiece off one Rory Kleinveldt over, then Hussey took a couple of fours off Imran Tahir as the partnership passed 50.
Clarke plundered 13 runs off one Tahir over, including a brutal flat six, as the leg-spinner's miserable Test match continued.
But Clarke (38) fell lbw to Dale Steyn in the next over, a DRS review proving fruitless for the Australia skipper.
Hussey then added another 33 with Matthew Wade before getting cramped for room as he attempted to pull Morne Morkel in the last over before lunch.
Steyn took the catch, but by that time the lead already had a daunting look about it.
Wade was out for 18 shortly after lunch, caught behind off Morkel (three for 50), but James Pattinson (29 not out) and Hilfenhaus (18no) swung the bat to take Australia to their declaration total.
It was Pattinson's last action of the series, though, having been diagnosed with a side and rib injury which reduces Australia's bowling options as they push for victory.
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