Chasing a target of 181, the Proteas looked well on course thanks to a maiden T20I fifty from Lhuan-dre Pretorius (51) and fellow opener Reeza Hendricks (37).
Dewald Brevis struck three huge sixes on his way to a 16-ball 31, but with seven runs required off the final over, was caught on the mid-wicket boundary going for another maximum off the bowling of seamer Matt Henry.
Henry then also took the wicket of George Linde (10), brilliantly caught at the long-on boundary by Daryl Mitchell as the New Zealand paceman only conceded three runs in the final over.
Henry finished with figures of 2-19 in his three overs and claimed the player-of-the-series award for his 10 wickets in the tournament.
Earlier, the Black Caps posted a total of 180-5 with Devon Conway and Rachin Ravindra both top-scoring with 47 while opener Tim Seifert struck 30.
Lungi Ngidi was the pick of the Proteas bowlers with figures of 2-24 in his four overs.
Veteran leg-spinner Graeme Cremer has been recalled to Zimbabwe's T20I squad for the upcoming tri-series against South Africa and Namibia, with Sikandar Raza named captain of the 15-man squad.
Namibia have named a 16-man squad blending experience and youth for the inaugural T20I tri-series against South Africa and Zimbabwe in Windhoek from August 28 to September 6.
Pat Cummins has welcomed Australia's long-awaited return to South Africa, describing the Proteas as a "really strong side" as the visitors begin preparations for a three-Test series in October.
South Africa's preparations for the T20I tri-series in Namibia have suffered an early setback after all-rounder Jason Smith was ruled out with a right adductor muscle strain.
