The win puts New Zealand top of the 10-team table in the round-robin phase of the competition.
With four wins out of five games, New Zealand are back on top of the points table, while South Africa remain with one win out of six matches and are almost on the brink of elimination.
Chasing 242 at Edgbaston, New Zealand won with six wickets left in the last over.
Lockie Ferguson took three wickets as New Zealand impressed in the field at Edgbaston.
The Blackcaps are unchanged, while South Africa brought in Lungi Ngidi.
South Africa's last World Cup game in Birmingham was the epic 1999 semi-final.
The last time South Africa beat New Zealand in the World Cup was 1999, also at Edgbaston.
On the deciding Day Five of Dunedin Test, rain played the role of party spoilers. Similarly, on Day Five of Hamilton Test, rains washed out New Zealand’s hopes of winning their last Test and equalling the series.
As the South African side prepared to fly home following their 1-0 series win over New Zealand, Domingo reflected on the past year in which he guided the Proteas from 7th to 2nd in the world rankings.
South Africa, in the same 12-month period, defeated New Zealand (1-0, both home and away), Australia (2-1) and Sri Lanka (3-0).