Matthew Breetzke will resume on the fourth morning on 19 with batting partner Ryan Rickelton on 8 as South Africa look to post a total that will trouble Australia batting last.
The series is level at 1-1 and the winners will occupy top spot in the test world rankings, which Australia currently hold.
How much is required remains to be seen. This is the first time a test match has been played in October at Newlands and while it has been warm, there is not the baking heat of mid-summer to open cracks and cause the pitch to crumble.
"The further it goes into the game, I think it's only going to get harder and harder (to bat)," Australian Josh Inglis said.
"I'm not sure of a total (to chase). You don't want them getting too many more than maybe 200 or so. Obviously spinning a fair bit. We've got a new ball in 30 odd overs. So, yeah, hopefully we start well tomorrow."
Aiden Markram was the first batter dismissed when he picked out mid-off Travis Head from the bowling of Mitchell Starc (2-29) for 1, before David Bedingham (11) was out on the pull for the second innings in a row and caught by Nathan Lyon off Josh Hazlewood.
Marques Ackerman made a bright 62 from 80 balls, his second half-century of the test after 95 in the first innings, but was cramped up by a Starc bouncer and caught at slip by Cameron Green.
Ackerman was furious as he left the pitch having wanted to review the decision, but was out of time having made the required signal to do so as the clock hit zero. That saved his side a review as replays showed he was out.
South Africa looked to be going to the close without further trouble until captain Temba Bavuma played a poor shot off spinner Lyon in the penultimate over of the day and was bowled for 35.
Inglis earlier equalled his career best score of 102, reaching his second test ton off 132 balls to help Australia to 429 in their first innings, a lead of exactly 100.
He was eventually out when wicketkeeper Rickelton caught him off the bowling of spinner Simon Harmer (4-104)
Alex Carey (80) also made a sizeable contribution, before Cooper Connolly was the last man out for 29, caught and bowled by Marco Jansen (3-60)
The series is level after Australia won the first test by 214 runs in Durban and South Africa responded with a victory by an innings and 31 runs in Gqeberha.