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Kiwi goalkeeper Sally Rutherford made a series of saves, as did SA keeper Mariette Rix, in a game full of passion and excitement.
Samantha Harrison’s field goal, however, provided the game breaker for the Black Sticks after she broke out against the run of play to strike with a field goal after 20 minutes.
That was New Zealand's first shot at goal, while South Africa had already had six on target, though they failed to convert their chances.
Earlier, world number 16 Belgium pulled off a sensational 1-0 win over third-ranked Germany.
New Zealand moved to the top of the table, on six points, ahead of Germany and Belgium.
The South Africans, who lost their opening match 5-1 against the hosts, were left trailing at the bottom of the standings.
They face Belgium on Sunday, while Germany square up against the Kiwis in the last match of the round-robin tournament.
