They beat Colombia 1-0, the goal coming from Amber Hearn after half an hour.
However, the Football Ferns, ranked 17th, seven places higher than the South Americans, finished with 10 players, and survived a late scare to keep themselves alive in the tournament.
Captain Abby Erceg was sent off by referee Gladys Lengwe from Zambia, in an appalling decision after a Colombian attacker tumbled spectacularly just outside the penalty box.
The New Zealand players protested the decision but Lengwe was unmoved. The players got their arms tangled briefly before the Colombian hit the ground.
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.
