At lunch on the third day the visitors were 183 for two in their second innings, an overall lead of 181 with eight wickets in hand.
Dean Elgar was on 69 and JP Duminy was on 74, the pair having added 138 for the third wicket after the Proteas lost two early second innings wickets late on the second day.
Duminy and Elgar were given few problems by an Australian attack which appeared to be wilting in the heat, with first innings destroyer Mitchell Starc struggling with his control and looking little like the player who claimed four wickets on the opening day.
Elgar's only real moment of concern came on 68 when Mitchell Marsh produced a big lbw appeal, but replays showed the ball was passing well over the stumps.
On 65, Duminy inside edged a delivery from Josh Hazlewood, clearly the most threatening of the Australian bowlers, into the ground and over his stumps.
The South Africans produced some elegant shots, but had clearly set themselves to bat all day in the heat and build a commanding lead.
They will be one bowler down in the Australian second innings, with champion quick Dale Steyn expected to be out for at least six months due to a shoulder problem which is likely to require surgery.
That they could be in such a strong position was remarkable given they appeared to be all but out of the match 24 hours earlier.
After winning the toss and being dismissed for 242, the South Africans appeared certain to be facing a massive first innings deficit when Australia cruised to 158 for none before lunch on day two, but the home side then collapsed in stunning fashion to make just 244.
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