After adding to his first-innings 190 with 82 in the second, Renshaw had Temba Bavuma caught at bat-pad late 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 offspin, and came in a match where he remains the only player to pass 50 with the bat in Durban.
It also headlined a big final hour for Australia in the field, after Aiden Markram (45no) led the Proteas' resistance to 1-73 in pursuit of a world-record chase.
Following on from getting a hooking Ryan Rickelton caught behind early, Josh Hazlewood (2-20) also had David Bedingham lbw for 46 with a ball that seamed back in.
Pat Cummins then had the out-of-sorts Tristan Stubbs caught behind needlessly driving, on a rare day at Kingsmead Stadium where bad light did not stop play.
Cummins' wicket capped a somewhat dramatic day for Australia, where Steve Smith was hit in the head 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 6-314 declared 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.
This was a different type of innings to the one that took Australia from 6-124 to 390 in the first innings, but was still vital.
"He didn't miss one sweep (all match). Even the lbw shout he still got glove to it," Maharaj remarked on Monday.
"He played very well. From the first innings to the second innings he was quite clear in his game plan and never deviated from it.
"If you take that (first) innings away, it could be a different outcome."
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's fastest ever innings of more than 300, and allowed Marnus Labuschagne, Smith, Renshaw and Beau Webster to continue the charge with a runrate of 5.41.
Renshaw's 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, but he also produced one imperious strike back over spinner Harmer's head for six.
"Everybody knows his talent, and we saw glimpses of it today," said Webster, who made an unbeaten 43-ball 39.
"He is quite destructive when he gets going, he hits the ball in some odd spots, and when gets in some moods he is really hard to stop."
Josh Inglis 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 on 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.
