John Smit's side were 14-3 ahead at the break, but found their lead threatened in the second half as Stephen Donald kicked the All Blacks back into contention.
In the end, it took a piece of quick thinking from No 8 Pierre Spies as he capitalised on a loose pass to hack the ball up field and help create a match clinching try for Jacque Fourie - his 27th Test strike and another vital score in the same mould as his second Test score against the Lons in Pretoria.
That was the second try of the game from the home side following a first-half effort from outside half Ruan Pienaar who was sent over in the left hand corner after good approach work from the Munster-bound Jean de Villiers.
In response the All Blacks could only conjure up one try of their own, from impressive centre Conrad Smith, who took full advantage of some poor tackling to race 20 metres to score in the first-half.
But the whistle of world cup final referee Alain Rolland too often caught out the visitors at the breakdown and All Blacks' skipper Richie McCaw was more than matched in that area by home hero Heinrick Brussow.
As well as outscoring New Zealand, who had kicked-off their campaign with a home win over Australia the previous weekend, 2-1 on tries, the Springboks also won the battle of the boots as their three goalkickers - Pienaar, Frans and Morne Steyn - landed six penalties to Donald's four.
The two teams meet again in South Africa this weekend before the world champions host Australia on home soil.
Scorers: South Africa: Tries: R Pienaar, J Fourie; Pens: M Steyn 3, F Steyn 2, R Pienaar. New Zealand: Try: C Smith; Con: S Donald; Pens; S Donald 4
South Africa: Francois Steyn; JP Pietersen, Jaque Fourie, Jean de Villiers, Bryan Habana; Ruan Pieenar, Fourie du Preez; Tendai Mtawarira, Bismarck du Plessis, John Smit (capt), Bakkies Botha, Victor Matfield, Heinrich Brussouw, Juan Smith, Pierre Spies
Replacements: Chiliboy Ralepelle, Jannie du Plessis, Danie Rossouw, Ryan Kankowski, Ricky Januarie, Morne Steyn, Wynand Olivier
New Zealand: Mils Muliaina; Joe Rokocoko, Conrad Smith Ma'a Nonu, Sitiveni Sivivatu; Stephen Donald, Brendon Leonard; Tony Woodcock, Andrew Hore, Neemia Tialata, Brad Thorn, Isaac Ross, Jerome Kaino, Richie McCaw, Rodney So'oialo
Replacements: Keven Mealamu, Owen Franks, Jason Eaton, Kieran Read, Piri Weepu, Luke McAlister, Cory Jane
Referee:Alain Rolland (Ireland)