Kane Williamson created more history on Tuesday afternoon as he became just the fifth New Zealander to score two centuries in the same test as the Black Caps continued to grind down South Africa in the first test in Tauranga.

Kane 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.

Kane was eventually stumped for 109, as New Zealand closed the day at 179/4, 528 runs ahead.

The purple patch continues for the kiwi skipper, who has now scored five centuries from his last 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 after dismissing South Africa for just 162 in their first innings with a mammoth lead of 349 runs.

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 Matt but the ball just managed to shave his pad and the finger was raised.

Ruan 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.

A Kapa Haka performance marked Waitangi Day at the lunch break on day three. Photo: Black Caps Facebook.

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 Mitch for just five as South Africa lost their ninth and Mitch claimed his 50th test wicket.

Rachin'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.

Mitch would end with figures of 3/34 while Henry claimed 3/31.

Matt 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 Dane had him trapped LBW for just three.

Devon Conway and Kane 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, Kane, 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 Kane's dismissal, Tom Blundell joined Mitchell in the middle with the pair surviving until stumps, Mitchell 11 not out and Neil on five.

Black Caps coach Gary Stead told TVNZ Kane'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."

Gary says 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."

Jonty Dine/RNZ