The Black Caps continue to heap misery on the touring Proteas, while Kane Williamson created more history on Tuesday as he became just the fifth New Zealander to score two centuries in the same test.
New Zealand further ground down the tourists on day three of the first test in Mount Maunganui - skittling them for 162 in response to their own imposing 511.
They are 528 runs ahead, with the likelihood of a declaration to come early on Wednesday.
Williamson backed up his 118 in the first innings by blitzing his way to a 31st test century off only 125 balls late on day three.
The 34-year-old was eventually stumped for 109 off Proteas skipper Neil Brand, as New Zealand closed the day at 179-4.
The purple patch continues for the veteran former skipper, who has now scored five centuries from his past eight innings.
The Proteas will need to create history of their own if they are to win this test as they will require the highest ever successful fourth innings chase.
New Zealand opted not to enforce the follow-on in the second innings, with coach Gary Stead saying it was a priority to preserve the fitness of his bowling attack, who he said would benefit from a longer period with their feet up ahead of next week's second test followed by two tests against Australia.
It took just five overs for the hosts to pick up their first scalp of the morning, as David Bedingham tried to pull a short Matt Henry delivery only to top edge it into the safe hands of Mitch Santner.
Just two balls later, Ruan de Swardt looked to leave Henry but the ball just managed to shave his pad and the finger was raised.
De Swardt reviewed but replays showed just enough of the stump clipped as the Proteas found themselves in a deep hole at 83/6.
A stubborn 17-over stand saw some resistance from the tourists before Clyde Fortuin nine-run 52-ball stand ended when he chipped one straight to short cover.
Approaching a half century, Keegan Petersen threw his wicket away as he tried to launch Rachin Ravindra out of the ground, only to find the New Zealand captain at mid-off.
Having taken a wicket with his first ball in test cricket, debutant Tshepo Moreki couldn't produce the same magic with the bat, clean bowled by Santner for just five as South Africa lost their ninth and Santner claimed his 50th test wicket.
Ravindra's golden summer continued as he wrapped up the first innings with a flighted delivery which beat Dane Peterson all ends and crashed into the off stump.
Santner would end with figures of 3/34 while Henry claimed 3/31.
Henry told TVNZ that accuracy and building dots has been the key to success with the ball.
"That first hour really set the tone for us, we were able to create pressure, we talked about that last night, when you build pressure it can be very tricky to score runs out here and the wickets came from that."
In their second innings, the Black Caps lost Tom Latham early as Petersen had him trapped LBW for just three.
Devon Conway and Williamson put on 92 for the second wicket, before Conway was caught for 29 looking for back to back sixes.
Trying to increase the run rate, Rachin Ravindra couldn't back up his first innings heroics and held out to short cover for 12.
With only three overs remaining in the day, Williamson, on 99, rocked back in his crease and cut Neil Brand away for a single to create history with back to back tons.
He now sits 13th on the all time list for centuries in tests.
After Williamson's dismissal, Tom Blundell joined Mitchell in the middle with the pair surviving until stumps, Mitchell 11 not out and Blundell on five.
Black Caps coach Gary Stead told TVNZ Williamson's innings was another great on a long list of memorable knocks.
"It's pretty special, he's been an incredible player and keeps churning out the runs, it's just fantastic for the team."
Stead said they chose not to make South Africa bat again in order to refresh his bowlers.
"We just felt this is the first of four test in a quick period so we wanted our bowlers to have an element of freshness, we looked at the amount of time left in game and wanted our guys to have asleep tonight and come back fresher tomorrow."
-RNZ