Fresh off adding to his first-innings 190 with 92 in the second, Renshaw had Temba Bavuma caught at bat pad in the final hour as the hosts fell to 4-102 in pursuit of 421 on day four.
The wicket was the first of Renshaw's Test career with his off spin, and came in a match where he remains the only player to pass 50 with the bat in Durban.
Pat Cummins then had the out-of-sorts Tristan Stubbs caught behind needlessly driving, after Josh Hazlewood claimed the opening two wickets.
Aiden Markram remains the lone resistance for the hosts, who are desperately trying to hold on in this Test rather than pull off a world-record chase.
The other positive for Australia was bad light not intervening, after Markham and David Beddingham (46) had taken the Proteas to 1-73.
The final hour capped a somewhat dramatic day for Australia, where Steve Smith was hit in the head while batting and did not field while being assessed for concussion.
His head knock, Renshaw's 82 and Nic Maddinson's free-wheeling 48 in Australia's 6(dec)-314 will leave selectors with decisions to make for Sunday's second Test.
But more immediately a crucial 1-0 lead is on offer in this three-Test series, against a South Africa side looking every bit like one that has not played for 10 months.
Renshaw's runs on Monday were another picture of a man comfortable playing spin in the middle order, as he reverse-swept and drove on either side of the wicket at will.
Tasked with keeping Australia's innings moving, he hit seven boundaries and two sixes down the ground off spinners Simon Harmer and Keshav Maharaj.
But for Renshaw to remain in the middle order Maddinson will likely need to stay in the side as an opener.
The left-hander's selection was heavily criticised following a first-innings 33-ball duck, but he did himself some favours with a blazing 38-ball 48 on Monday.
That set the platform for Australia, and allowed Marnus Labuschagne, Steve Smith and Renshaw to continue the charge.
His intent was obvious when he hooked Marco Jansen for four on the first ball, before clearing the legside rope off Wiaan Mulder as light faded on day three.
Some shots were streakier than others as he went hard at the quicks outside off stump, but he also produced one imperious strike back over spinner Harmer's head for six.
Josh Inglis has landed in South Africa and batted in the nets on Monday as he continues his recovery from a fractured finger, while Cameron Green is fighting to overcome an abdominal strain.
There is also the prospect of uncertainty around Smith. He shook off a blow to the side of the helmet from Anrich Nortje to hit the quick for three straight boundaries a few overs later and went on to make 27.
Australia must now wait to see if he passes concussion tests and is able to take his place at Gqeberha next Sunday.
Labuschagne, meanwhile, was frustrated to be out for 37 off 58 for a second straight innings when he hit Maharaj to cover.
The Queenslander looked good until then, and has now scored between 30 and 70 in seven of his 14 innings since returning to the Test side last summer.
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