Australia will resume on Monday at 0-33, with a 139-run lead and appearing the only team with any realistic chance of winning the first of three Tests.
The biggest barrier could still be Durban's early sunsets and afternoon cloud cover, with bad light ending each day early and Australia needing enough time to win the match.
Australia showed their intent on Sunday evening by scoring at just under a run a ball, with Nic Maddinson hooking the first ball from Marco Jansen for four.
Maddinson also hit Wiaan Mulder for six over the legside late in the day, with Australia eying off setting a fourth-innings target and having enough time to bowl South Africa out.
"We might see a lot more of what we saw this evening from their approach," South Africa's batting coach Ashwell Prince said.
"You've got to look to take wickets. At the same time, you've got to control the run rate.
"You might say, well, you're trying to cover both ends. In the first innings, they put a big score up on the board, but they went at 2.8 runs and over, 2.9 runs and over.
"We'll see a few more of the spinners tomorrow. Maybe a few innovative field placings and put the ball in their court to come and play."
Prince refused to be overly critical of his side's batting on Sunday, despite them throwing away a good start of 1-84 in reply to Australia's 390 with a slew of loose shots.
Tristan Stubbs (32) and Mulder (30) were both out taking on Cummins' short balls in the space of two overs.
It was hard to determine which stroke was worse.
Mulder appeared to withdraw from his pull shot before ballooning the ball to square leg, while Stubbs' dismissal, hooking at fine leg, was extra frustrating given what had just happened.
Marco Jansen also fell trying to pull Josh Hazlewood six overs later, while Temba Bavuma and Kyle Verreynne were both smartly caught at slip by Steve Smith trying to reverse sweep.
What South Africa desperately needed was someone to play the long game, just as Matt Renshaw did for Australia to rescue them from 6-129 to 390 on the opening two days.
Prince would not be critical of individual shot selection, but indicated they needed to work harder to grind Australia down.
"Australia going to come with a certain intensity that can only last for a certain period of time," the former South Africa captain said.
"Sometimes you've got to be able to absorb that intensity until you take the sting out.
"Every time a wicket falls, it energises the bowling attack and they feel that they can push on a little bit more.
"(But) you might go to a fourth seamer or you might go to a part-time spinner earlier if a partnership is extended."
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