Visitors were reduced to 80 for five in their second innings at the close of day four, with captain Faf du Plessis and wicketkeeper Quinton de Kock were each not out on 15 and tasked with the rescue job.
3rd Test: Latham shines against SA in New Zealand gloom
Proteas are still 95 runs behind New Zealand’s first innings score of 489 at Seddon Park, which means they need nothing less than a miraculous performance to save the Test from here on.
South Africa lead the series 1-0 after an eight-wicket victory in the second match in Wellington.
The Proteas' middle and lower order have proved difficult to dislodge throughout the series but their top order again failed to provide a foundation.
New Zealand DRS bungle aids Proteas in the rain
After Dean Elgar chased a swinging delivery from Colin de Grandhomme and was caught by wicketkeeper BJ Watling, it was a steady stream of specialist batsmen back to the pavilion. Theunis de Bruyn was run out in comical circumstances when he and Hashim Amla collided attempting a single, while Amla attempted to cut a Jeetan Patel delivery only for the ball to rebound off Watling's gloves to De Grandhomme at first slip.
JP Duminy then failed to play at a Patel arm ball and was bowled before Temba Bavuma completed the misery for the top six when he played a loose stroke to a Matt Henry delivery and was caught by Watling to leave the visitors 59 for five.
The hosts were dismissed for 489 before tea with the lead of 175. De Grandhomme was the last man out, as he departs after scoring his maiden half-century and finished with score of 57.
De Grandhomme had joined Watling after lunch following Mitchell Santner's dismissal for 41 in the final over before the break.
The situation was tailor-made for the fast-scoring right hander, with New Zealand having struggled against a tight South Africa attack in the first session.
Watling and Henry both fell while trying to attack left-arm spinner Keshav Maharaj before Patel was bounced out by Kagiso Rabada with the third new ball.
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