Chasing a moderate 152 to win, after New Zealand were sent in to bat first, the hosts went about putting together good partnerships to ultimately reach the target with 13 balls to spare.
Hashim Amla produced a workman-like 48 from 41 with Rilee Rossouw providing a couple lusty blows at the other end as the pair marched towards the victory.
Rossouw (38, 20 balls) skied a shot with less than 10 required for the win as New Zealand were gifted a wicket. With five to win, Amla threw away his wicket in similar fashion as he skied a shot off the bowling of Adam Milne to be caught at square leg running in.
David Miller (2) and Farhaan Behardien (4) were the batsman in the middle who took the Proteas over the line.
Earlier, AB de Villiers played a trademark innings where he steadily increased the scoring rate. After striking five boundaries quite effortlessly, the Proteas star-batsman holed out to George Worker off the bowling of Nathan McCullum for 33 off 21 balls.
Regular Proteas T20 captain, Faf du Plessis picked up a left-knee injury shortly before the game and De Villiers took over the captaincy role. In the place of Du Plessis, Morne van Wyk came in and handled the wicketkeeping duties.
New Zealand got off to a flier in their innings with Martin Guptil and captain Kane Williamson picking off the South African attack with ease.
South Africa made the breakthrough in the eighth over as spinner Aaron Phangiso (2/29) outfoxed the Kiwi skipper. Phangiso removed Williamson for 42 off 21 balls, as the batsman came down the track but missed the ball and Van Wyk whipped off the bails as the visitors lost their first wicket for 68.
The Kiwis were still in a good position with Guptill in the middle, but the New Zealand opener threw away his wicket by not sliding his bat in properly and was run out by some swift glovework by Van Wyk. New Zealand were reduced to 102 for two after 12.3 overs, and a steady procession of wickets followed.
Kagiso Rabada 2/28, David Wiese 2/24 and Phangiso were the bowlers to strike for South Africa as New Zealand were restricted to 151 for eight, when a score around the 200 mark seemed likely earlier in their innings.