Chasing a target of 174, the Proteas lost wickets at regular intervals and were eventually 152 all out in 18.2 overs.
Lhuan-dre Pretorius got the run-chase off to a rapid start with 27 off 17 balls but was dismissed by seamer Matt Henry in the fourth over.
The Proteas then slipped to 62-5 as there no further contributions before Dewald Brevis and George Linde came together to get the side back into the contest.
The pair added 39 with Brevis striking 35 off just 18 deliveries before Henry again made the crucial breakthrough for the Black Caps.
Rassie van der Dussen's charges were still well in the game as Linde (30 off 20) and Gerald Coetzee (17) added 37 together but the former holed out to mid-wicket with 26 runs still needed.
The match was done in the penultimate over when, fitting, Henry took the final wicket as Coetzee went for a slog but was caught in the deep to give Kiwis the victory.
Earlier, New Zealand posted a total of 173-5 that was built around an unbeaten 103-run partnership between Tim Robinson and debutant Bevon Jacobs.
The pair came together when the Kiwis were struggling at 70-5 but Robinson struck 75 not out from 57 balls and Jacobs an unbeaten 44 off 30 deliveries to make sure they got to a more than decent total.
Senuran Muthusamy wants to embrace the challenge of putting in consistent performances at the highest level as he chases a place in the Proteas squad for next year's T20 World Cup.
New Zealand made it two wins from two in the T20I tri-series in Harare after dispatching host nation Zimbabwe by eight wickets on Friday.
New Zealand all-rounder Glenn Phillips has been ruled out of the T20I tri-series in Zimbabwe involving the Proteas and the subsequent Test series after sustaining a groin injury during the Major League Cricket final.
Cricket South Africa has appointed Patrick Moroney as the new Convenor Selector for the Proteas Men's Team.
