Dismissed for 214 in response to the hosts' 481 for eight declared, the visitors' recent victories against Zimbabwe looked distant.
The bowling attack responded to have South Africa reeling at 105 for six by stumps, but the coup de grace appeared to be struck.
The hosts lead by 372. The highest fourth innings chase in 21 previous tests at the ground was England's 251 for eight in January 2000. Conservatism from stand-in skipper Faf du Plessis in his second test in the role is understandable, but the Black Caps' prospects of a first series victory against the Proteas look to have evaporated. The chances of a drawn series also appear slim, but this New Zealand side has earned the right not to be written off.
Captain Kane Williamson's defence, as part of 77, was the thread which kept them from completely unravelling as Dale Steyn (three for 66), Kagiso Rabada (three for 62) and Vern Philander (two for 43) weaved their magic.
Henry Nicholls accumulated 36 - the second time in seven innings he's pushed beyond the teens - before Rabada trapped him lbw around the wicket. Umpire Paul Reiffel gave it not out, but a review corrected a plumb dismissal.
Nicholls took three cheap boundaries over the slips from Steyn's second over of the day, before receiving a nostril-tracking missile in retaliation. He looked accomplished off his legs and the back foot at times, but doubts remain over his technique.
However, like any previous selection of the Mike Hesson tenure, expect Brendon McCullum's No 5 successor to get plenty more opportunities in India and at home to make a thorough judgement of his test character.
To complete an awkward umpiring morning, BJ Watling was given not out by Ian Gould on eight, only for the review to show a glove had edged it behind off Steyn.
Mitchell Santner had his bails shattered for a duck by a Philander in-swinger.
Neil Wagner's cameo of 31 from 30 in a 45-run ninth-wicket stand gave a flaccid innings pep. His negotiation of a short-ball barrage from Rabada was compelling.
At the other end, Williamson had eased into his cricketing element, particularly dueling against Steyn. A point blank parp from a vuvuzela would have struggled to rattle his concentration.
Steyn is arguably the most attacking bowler in cricket's top echelon. Of the 13 players to pass 400 test wickets, he has the lowest strike rate of 42. No one else is under 50. His injury worries of recent months have coincided with South Africa's slide to seventh in the test rankings.
You sensed Steyn relished the challenge against Williamson, someone he would consider a worthy opponent for his bowling venom.
The New Zealand captain responded with hands of velvet and the judgment of a bomb disposal expert outside off stump, rekindling memories of his 2012 century from 228 balls and almost five-and-a-half hours against South Africa at the Basin Reserve.
A cracked box from that ordeal, apparently signed by the perpetrator Steyn, is understood to sit in Williamson's memorabilia vault.
The 26-year-old reached 40 at lunch and had advanced to 77 when he unsuccessfully attempted to pull Rabada, shortly after No 11 Boult's arrival.
No New Zealander had scored centuries against all test-playing countries until Williamson completed his 113 against Zimbabwe this month. He fell 23 runs short of being the first of his countrymen to score centuries against all test-playing nations... away from home.
Tim Southee and Trent Boult revived New Zealand's flatlining presence with two wickets apiece to rock South Africa at 47 for four in the 12th over after du Plessis opted not to enforce the follow-on. Further local embarrassment was staved off via opener Quinton de Kock's 50, and No 6 Temba Bavuma, who was 25 not out at the close.
With two days remaining, New Zealand have plenty of toil ahead to force their way back into the match. If that is to happen it will start with someone, anyone, matching Williamson for defensive batting pluck.
