Set an intimidating victory target of 539, the home side were wobbling on 169 for four at stumps and facing a potential record defeat against South Africa.
Usman Khawaja was on 58 and Mitchell Marsh on 15, with South Africa’s unbeaten record at the ground set to be extended.
An extraordinary piece of fielding by the diminutive Temba Bavuma removed the dangerous David Warner for 35 to end an opening stand of 52.
Warner dropped the ball in front of him and set off for a quick single, but Bavuma pounced from cover and unleashed a powerful throw while horizontal and still in mid-air.
It rattled the stumps at the non-striker’s end with Warner centimetres out of his ground.
The dismissal set the stage for Rabada (three for 49) to display his quality in the absence of champion pacemen Dale Steyn due to a shoulder injury suffered on the first day.
Four balls later fellow opener Shaun Marsh (15) was caught at second slip by Faf du Plessis off the bowling of Rabada as Australia suddenly slumped to 52 for two.
Things appeared to get even darker for the hosts when new batsman Khawaja was given out caught behind first ball against the part-time spin of JP Duminy.
A decision review saved Khawaja when it showed the ball had glanced off his pad rather than the bat.
Steve Smith and Khawaja, who was dropped on 41 when Hashim Amla could not cling on to a tough chance at first slip, set about rebuilding the Australian innings in search of a draw.
The pair settled in against the part-time bowlers, but when the ball started to reverse swing Rabada returned to the attack and ended a 92-run third-wicket stand with an impressive spell.
Bowling with high pace in his ninth Test, the 21-year-old showed he can become the perfect long-term replacement for Steyn when he removed Smith (34) and Adam Voges (1) in successive overs.
Smith had looked solid but drove at a ball and got an outside edge to wicketkeeper Quinton de Kock.
Rabada’s next over to Voges was outstanding, with a couple of almost unplayable deliveries before he had the new batsman caught behind off a thin outside edge.
South Africa bowling coach Charl Langeveldt was thrilled with Rabada and said the over to Voges gave him goosebumps.
“He’s done it before, today he stepped up again,” he said.
“When you are bowling spells at 145 kilometres an hour that is always exciting.
“That (over to Voges) is why we are promoting Test cricket, it gave me goosebumps in the dugout.”
With Steyn absent and little assistance for the spinners, Langeveldt said carefully rotating Rabada and Vernon Philander would be the key to success on the final day.
A disappointed Australian fast bowler Peter Siddle maintained there was still hope for the home side.
“It is deflating to be in the position we are in, we’re in a hard place,” he said.
“But we can always dream ... stranger things can happen if you drag them out to late on day five and we know they are a bowler down.”
South Africa had declared their second innings on 540 for eight after lunch when Philander was bowled by Smith for 73.
It ended a brisk 72-run stand with Keshav Maharaj (41 not out) as the visitors batted the home side out of the match after resuming on 390 for six on Sunday morning.
South Africa’s massive total was underpinned by 141 from Duminy and 127 from Dean Elgar.
The pair put on 250 for the third wicket as part of a remarkable comeback by the tourists after their disappointing first day.
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