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.
Temba Bavuma is "all good" and should be ready to take the field when Australia arrive on South African shores for the three-match ODI series next month, according Proteas coach Shukri Conrad.
Bjorn Fortuin has been selected as captain of the Proteas 15-man squad for the white-ball tour to Namibia, starting later this month, with Temba Bavuma (ODI) and Aiden Markram (T20I) being rested.
Fast bowler Kagiso Rabada is adamant that playing the 2027 ICC Men's Cricket World Cup on home soil will not add any additional pressure on the Proteas to perform.
The Proteas will travel to Namibia later this month for a T20I tri-series, that will also include Zimbabwe, which will then be followed by three ODI matches.
