An explosive spell before lunch on day four by Proteas spearhead, Dale Steyn, set up an emphatic series clinching victory for the hosts at Supersport Park.
It took just two over from Steyn to have New Zealand five for three after skipper Faf du Plessis had earlier declared with his men on 132 for 7 sporting a 399 run lead.
Steyn got both openers for ducks in his first over and picked up the wicket of Ross Taylor, in his next to leave the Black Caps reeling.
Vernon Philander picked up the wicket of New Zealand's rock, Kane Williamson, as it seemed the Proteas would run through their visitor's in no time at all.
BJ Watling and Henry Nicholls offered stubborn resistance after lunch, before Dane Piedt Trapped the wicketkeeper leg before for a patient 32.
Watling's was the only wicket to fall in the afternoon session, but after tea the Proteas cranked it up a gear.
Steyn cleaned up Mitchell Santner, beating him for pace and dislodging his middle stump.
Doug Bracewell was aggressive, and scored 30 off 36 balls, before Vernon Philander trapped him leg before, The big Kiwi reviewed but the replays couldn't save him and he had to go.
Tim Southee had a brief hit out but a Kagiso Rabada yorker did him in for 14, and the quick trapped Wagner leg before soon after to put the Proteas on the brink of a series win.
Fittingly it was Steyn who got the final wicket as Nicholls holed out to the long leg boundary to give the Phalaborwa Express his five-for.
Steyn finished with figures of 5 for 33 with Nicholls top scoring with a score of 76 as New Zealand finished on 195 all out.
South Africa won by 205 runs and took the series 1-0.