The sole goal of the match came via forward Amber Hearn in the 31st minute.
The win gives them three points from two games in their group G.
The format of the tournament, three groups of four teams, has the top two in each pool progressing to the last eight, along with the two best performing third-placed teams.
Winning keeps New Zealand in medal contention going into their final group match against formidable world No 3 France.
However their problem lies in the state of the other two groups.
Brazil, Sweden and China all have three points in group E, and the first two named play later today, and South Africa have none.
Canada have six points in group F with Germany four, Australia one and Zimbabwe none.
World No 5 Australia have the fillip of facing Zimbabwe in their last game on Wednesday and would expect to get to four points.
So New Zealand have their hands full with a tough finale.
Still, coming after their disappointing 2-0 loss to the world No 1 United States last week, the New Zealanders will be pleased with the outcome. On rankings, they should have won it too, but the loss of the experienced Erceg is a stinging blow.