Tim Paine receives treatment for his broken thumb.
Elgar will resume on the fourth morning, with his captain Faf du Plessis on 34, as the pair look to increase the lead towards the 500-run mark.
Dean Elgar amassed 39 from 158 balls in a patient knock that has been the glue for South Africa's second innings.
Australia opted against naming a vice-captain for the fourth Test against South Africa, with the sacking of Steve Smith and David Warner igniting a leadership crisis. Thus, prior to the start of play and just after the completion of the national anthems of both sides, Tim Paine and the rest of his Australian side went ahead and walked past the Proteas in a bid to shake their hands, something that he was lauded for and depicting a hallmark of his sportsmanship.
Wicketkeeper Paine picked up his injury while standing up to the stumps for seamer Chadd Sayers on the second day, but has been able to continue in the match and has provided dogged resistance.
However, the skipper continued to keep in Johannesburg and later even came out to bat, when Australia had collapsed to 5-96.
Paine was last man out to a running, diving catch by Elgar, which gave the innings a gripping finish.
Vernon Philander, Rabada and Maharaj picked up three wickets each for the hosts, while the other wicket went to Morkel, who had dismissed Mitchell Marsh on Saturday. Their partnership ended as Cummins was trapped leg before wickets by Keshav Maharaj. Cummins has maybe the biggest claim to be Australia's best player on one of its worst tours considering the stunning fallout from the cheating scandal.
The home side have a fitness worry as seamer Morne Morkel, playing in his final test before retirement from global cricket, was forced from the field with a left side strain, but he did return to the pitch after the interval and will be monitored overnight.
"We've got to try and take some sort of positive out of it long term and turn ourselves into the cricket team we want to be".
The busted digit is on Paine's right hand, where his index finger serves as a constant reminder of an injury that threatened to end his career after it was broken by a 148.2 km/h thunderbolt from Dirk Nannes in 2010.