South African pace trio Kagiso Rabada (3-81), Vernon Philander (2-26) and Morne Morkel (4-87) had worked over Australia's batsmen superbly, the latter surpassing 300 Test wickets in his final series.
The tourists, as a result, still do not have a century-maker in their midst on this tour and the top six are all averaging below 40. They are on the back foot, although the contribution of Lyon and Paine enhanced confidence.
An unshakable Tim Paine improved morale.
"Those runs at the end were vital, in terms of the game, so we're back in the game," Australian coach Darren Lehmann said.
"We've certainly going to have to bowl better in the second innings. I don't think we bowled that badly but we can certainly improve in that area. But our top-order batting has to improve. There is no doubt about that."
Australia were left without their two best batsmen inside the first 16 overs after David Warner's quickfire 30 from 14 balls was halted spectacularly by Rabada, who sent his off stump hurtling in the direction of the Wynberg End boundary, and Steve Smith's modest series continued.
Nathan Lyon went out swinging.
In the meantime, Usman Khawaja (5) also failed to make an impression, coming unstuck with a pull shot off Morkel that was swallowed up by Rabada at fine leg.
Smith, was also undone by the bounce of Morkel on five, caught by Dean Elgar at gully after a leaping ball found its way to the shoulder of his bat.
It was the captain's first single-figure performance since the Adelaide Test against England last December and his series average dipped to 27, lower than he has managed in any since his debut series against Pakistan in England in 2010.
Smith's dismissal left Australia 3-71 soon after lunch and while Bancroft and Shaun Marsh (26) stemmed the flow of wickets their recuperative 79-run stand ended just before tea. Marsh, having looked in command to that point, flashed carelessly at a wider ball from Morkel and was caught behind.
Philander, whose formidable record at his home ground is highlighted by the demolition job he did on Australia in 2011, was also intent on getting in on the action from the other end.
In a top-shelf spell in which had the ball seaming and hooping away deliciously from the right-handers and his length was bang on, it seemed only a matter of time before he cashed in.
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When that moment did inevitably arrive, right on the stroke of tea, it came via a ball that nipped inwards and thumped Bancroft on his front pad. Ambitiously, the opener called for a review but the ball-tracking technology confirmed he was plumb.
Soon after the interval Mitchell Marsh – the latest to exit for five – was the victim of another Philander gem that caught his edge of his bat and arced into the gloves of Quinton de Kock.
Australia, having set out to exceed South Africa's total of 311, were left well and truly spluttering, losing 5-25.
The stuffing was taken out of Philander's fine outing when he face planted while trying to stretch out for a catch and was escorted from the field with whiplash.
With the 32-year-old absent for more than 30 minutes, Lyon and Paine's rearguard effort narrowed the margin.
"Tim played really well," Lehmann said. "Tim's probably been our standout batsman for the tour so far. the way he's played reverse-swing and played their bowlers."
An eventful second day also featured two world records being equalled simultaneously before it was an hour old.
Smith's five catches in an innings has never been bettered and only 10 others in history share the distinction.
Elgar, meanwhile, joined Desmond Haynes as the only player to have carried his bat three times as he wound unbeaten on 141 in South Africa's first innings. The 30-year-old opener has already achieved the feat twice this year.
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Chris Barrett is a Sports Writer with The Sydney Morning Herald.
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