After Josh Inglis's century helped Australia to 429 and a lead of 100 on Thursday, Aiden Markram and David Bedingham both threw their wickets away early.
Markram drove a good-length Starc ball straight to Travis Head on one, before Bedingham top-edged a hook off Hazlewood to Nathan Lyon on the boundary.
Bedingham's dismissal on 11 was particularly poor, after he was one of three Proteas bounced out hooking in a similar fashion in the first innings.
Starc and Hazlewood bowled a number of short rising deliveries in their opening spells, with Marques Ackerman (33no) and Bedingham both wearing balls on the body.
Things could have been worse for the Proteas, with Ackerman nearly run out twice after Temba Bavuma came to the crease.
The first of those was a near miss from Inglis, while Cooper Connolly then had an age to pull of a direct hit after a bad mix-up.
South Africa have not lost a home Test series for almost six years, but now need a recovery effort in a three-match contest full of twists and turns to keep that record alive.
Australia's charge with the ball comes after one of their most complete batting performances in years.
Inglis's century was complemented by 74 from Matt Renshaw and 65 from Cameron Green on Wednesday, before Alex Carey reached 80 on Thursday.
Connolly also made a crucial 29 alongside the lower-order, helping add another 49 for the final few wickets after Australia lost 3-10 on Thursday.
Those extra runs could prove crucial, with the pitch showing signs of turn and spinner Simon Harmer taking 4-107.
Inglis enjoyed the most important innings of his career after being called in late to replace Steve Smith, bringing up his ton when he reverse-swept Harmer to the boundary.
At that point the Proteas had started the day reasonably flat, with a number of misfields at Newlands under the warm Cape Town sun.
But when he was caught behind later in the same over and a 185-run stand with Carey was ended, the Proteas were suddenly back in the contest.
Carey edged Harmer to slip four overs later, before Pat Cummins was trapped lbw by Kagiso Rabada in the mini collapse.
Connolly then showed a glimpse of why he is so highly rated, building Australia's total alongside Starc (11) and Lyon (1).
Playing in just his second Test, the 23-year-old flayed one ball away over backward point for four off Gerald Coetzee.
The shot of the day also came off the right armer, when he drove a low full toss for four through the covers shortly before the break.Â
He played a similar shot from Jansen (3-60) after lunch, to a ball that wasn't all that full.
