The tourists declared at 6-314 when tea was taken, with Nic Maddinson's quick-fire 48 and Matt Renshaw's 82 setting up the innings.
Beau Webster also hit an unbeaten 39 and Pat Cummins 32no off 12 balls, as Australia decided to press on to a lead of beyond 400.
To win the Test South Africa would need to pull off the greatest chase ever achieved in the country, with the previous best mark of 340 set by the Proteas in 2002.
But the reality is Australia are the team playing for a victory in this Test, as they eye off a 1-0 lead against the world champions in the three-match series.
Technically there are a little over four sessions for Australia to bowl, but bad light has ended play at least one hour early on every day so far with a 6pm sunset.
That theoretically means the tourists should have around 100 overs to dismiss the Proteas.
Beyond this Test, Australia have decisions to make around Maddinson and Renshaw.
After Maddinson's selection was heavily criticised following a first-innings 33-ball duck, the left-hander blazed his way to a 38-ball 48 on Monday.
That set the platform for Australia, and allowed Marnus Labuschagne (37), Steve Smith (27) and Renshaw to continue the charge.
Renshaw reverse-swept and drove the spinners at will before being caught and bowled by Keshav Maharaj, backing up his first-innings 190 that set up the match for Australia.
After three innings in this Test, Renshaw is still the only player to pass 50, with his ability to handle spin strengthening the case for the Queenslander to stay at No.5.
For Renshaw to remain in the middle order rather than open, it would likely require Maddinson to stay in the team even if Josh Inglis or Cameron Green are fit.
Maddinson at least gave himself a chance at the selection table with the way he batted in the second innings.
His intent was obvious when he hooked Marco Jansen for four on the first ball, before clearing the legside rope off Wiaan Mulder as light faded on day three.
Some shots were streakier than others as he went hard at the quicks outside off stump, but he also produced one imperious strike back over spinner Simon Harmer's head for six.
Maddinson's return to the side after almost 10 years out sparked criticism from former players, but he now looks a better chance of staying than he did after day one.
Labuschagne, meanwhile, was frustrated to be out for 37 off 58 for a second straight innings when he hit Maharaj to cover.
The Queenslander has now scored between 30 and 70 in seven of his 14 innings since returning to the Test side at the start of last summer.
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