Renshaw shared crucial partnerships with Cummins and Lyon before Simon Harmer eventually dismissed him, and the hosts lost opener Ryan Rickelton for a three-ball duck late on Saturday.
The Proteas made steady progress on Sunday morning, with Aiden Markram and David Bedingham adding 84 for the second wicket.
Markram fell for 37 to Starc before Bedingham followed for 49, edging Cummins to Steve Smith.
SA skipper Temba Bavuma then made three before Lyon had him caught by Smith, leaving the Proteas on 99/4 at drinks.
Tristan Stubbs and Mulder, who had taken their side to lunch, responded with a 56-run, fifth-wicket stand, but Cummins broke through twice after lunch, removing Mulder for 30 and Stubbs for 32.
Lyon then dismissed Kyle Verreynne for 13 before Marco Jansen briefly shifted the momentum with an attacking 26 off 20 balls, including six fours, before Hazlewood put an end to his cameo at 197 for eight.
Harmer and Keshav Maharaj then produced SA’s most stubborn resistance of the innings, adding 52 for the ninth wicket.
Starc finally removed Maharaj for 34 shortly after tea, caught by Cummins, but Harmer continued to defy the attack, finishing unbeaten on 35 from 75 balls.
Anrich Nortje contributed 16 before Beau Webster had him caught by Smith to complete the innings at 284 in 77.6 overs.
SA’s top scorer was Bedingham with 49, while Markram’s 37, Harmer's unbeaten 35, Maharaj’s 34, Stubbs’ 32 and Mulder’s 30 provided enough resistance to ensure Australia had to work through the innings rather than run through the lower order.
SA lost nine wickets during the day, with four falling in the morning, three in the afternoon and the final two in the closing session, which makes Harmer and Maharaj’s 52-run stand all the more crucial in pushing the total beyond 250 and limiting Australia’s first-innings advantage to 106.
Their bowlers will need to be on point if SA are to salvage the game.
