Goalkeeper Erin Naylor then pulled off a fine one-handed save from the resulting free kick.
The Ferns were worth the win, which 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.
So the win keeps New Zealand in the frame, going into their final group match against the formidable world No 3 French.
However their problem is 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.
The US, who beat France 1-0, have six points in group E. France also have three points, but a superior goal difference to New Zealand, after their 4-0 win over Colombia in their first game. That gives them a +3 difference to New Zealand's -1.