On the back foot after falling to 4-140 at the end of day three, the Proteas lost just one wicket in the first two sessions on Friday to take back the upper hand.
Ryan Rickelton led the way for the hosts with an unbeaten 83 at tea, as part of an unbeaten 113-run sixth-wicket partnership with Wiaan Mulder (46no).
Australia have been unable to get any real purchase out of the second new ball, turning to Nathan Lyon after just five overs with it.
South Africa had said on Thursday they believed they could defend as little as 120, on a pitch offering plenty of turn with puffs of dust exploding.
Australia suggested they would want to keep the Proteas' lead to less than 200, while also believing time could be a bigger factor as the wicket wears.
The target is already approaching that with South Africa still having five wickets in hand, with Rickelton also showing a willingness to bat time.
He went nearly 30 minutes without scoring while on 24 on Friday morning, before three boundaries in the next three overs and a number of sweet drives after lunch.
Mulder has shown slightly more willingness to attack, including a slog-sweep for six off Lyon in the second session.
The largest fourth-innings target successfully chased at Newlands was 331 by Australia in 2002, with the next best being 236 by South Africa in 2011.Â
The Proteas were guilty of throwing away their only wicket in the opening two sessions, with Matthew Breetzke the fifth South African out hooking this Test.
Breetzke attempted to take on a shorter ball from Cummins and swiped the air with his bat in frustration, knowing he had let an opportunity go.
Cummins had endured the longest wait for a wicket in his Test career until that point, having bowled 374 balls and conceded 210 runs since his last scalp in Durban.
Fightbacks have been the theme of this series, with the No.1 spot in the ICC Test rankings on the line and the Proteas trying to remain unbeaten at home since 2021.
Australia were 6-124 in the first Test in Durban before Matt Renshaw's career-defining 190 hit them to 390 and a big win to start the series.
South Africa were then 6-110 in Gqeberha last week, before Temba Bavuma's century took them to 9-425 declared and Australia were flogged after being bowled out for 99 in reply.
Even in this Test, the Proteas reached 0-140 at lunch on the first day, before Starc's six-wicket haul put Australia back in the game and the tourists eventually claimed a 100-run first-innings lead.
Cummins' decision to bowl first may be back in the spotlight if they are unable to chase down a fourth-innings target on a deteriorating wicket.
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