South Africa were 105 for six at the close, an overall lead of 372 runs on a pitch at Centurion's SuperSport Park offering assistance to bowlers, with swing, seam and uneven bounce.
South African fast bowler Dale Steyn said his team would continue batting on Tuesday.
"The longer we bat, the longer the sun will bake on this wicket and the cracks will open wider. When you hit the deck there's always something happening here," he said.
New Zealand hit back after conceding a first innings lead of 267, with Tim Southee and Trent Boult taking two wickets each to reduce South Africa to 47 for four. Doug Bracewell and Neil Wagner also picked up wickets, with only Quinton de Kock shining for the South Africans, with his second half-century of the match.
Du Plessis ton puts South Africa on top
"It was a very pleasing last session for us," said Bracewell. "We spoke about giving it everything and we came out with plenty of energy."
But he acknowledged that New Zealand would have a difficult time batting last.
"It's a tough wicket to bat on, going up and down a bit," he said.
South Africa's three-pronged pace attack was mainly responsible for New Zealand being bowled out for 214 in their first innings.
Steyn and Kagiso Rabada took three wickets each and Vernon Philander claimed two.
With star bowlers Steyn and Philander both returning from long-term injuries, it was the first time they had played in the same Test match as Rabada, South Africa's 21-year-old cricketer of the year.
"It made a good combination," said Steyn.
Proteas in complete control on day one
"Vernon is a phenomenal bowler. He keeps it so tight so you feel free to run in (and attack) from the other end. And KG (Rabada) is bowling at 150 km/h and getting wickets."
The combination proved relentless, although it took South Africa more than an hour to take the first wicket of the day, when Rabada trapped Henry Nicholls lbw for 36.
Only captain Kane Williamson was able to provide sustained resistance for New Zealand. He was last man out for 77. While his teammates struggled, Williamson remained calm and well-organised, seemingly with time to spare as he combatted the pace threat. He batted for 286 minutes and faced 133 balls in an innings which included eight fours and a six.
New Zealand's resistance crumbled after the breakthrough, although South Africa lost control briefly when Rabada and Steyn peppered number ten batsman Neil Wagner with bouncers, probably in retaliation for Wagner's short-pitched assault during South Africa's first innings of 481 for eight declared.
South Africa, New Zealand Test drawn after abandonment
Wagner was struck on the helmet by Rabada but responded by slogging four fours and a six in an innings of 31 before he was caught behind off Steyn.
Off-spinner Dane Piedt picked up the wicket of Tim Southee, while Ross Taylor was run out during New Zealand's collapse on the second evening.
Three of the first five wickets came through successful reviews by South Africa after their initial appeals had been turned down.
After a maiden over from Southee to Stephen Cook to start the second innings, De Kock hit the first four balls of the next over from Boult for fours before hitting Southee for four and six off successive deliveries in the third over.
New Zealand hit back, however, with three wickets in 10 balls. Cook was trapped in front by Boult for four before Southee dismissed Hashim Amla, caught at first slip, and JP Duminy, lbw, in the next over.
Captain Faf du Plessis and De Kock tried to rebuild the innings, but first innings centurion Du Plessis made only six before he was caught at first slip off Boult.
De Kock seemed untroubled by the struggles of his teammates, going to his second half-century of the match off 42 balls, with eight fours and a six. But one ball later he received a vicious bouncer from Doug Bracewell which he gloved to gully.
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