Portia Woodman on the way to scoring her try. Photo: Reuters
After Portia Woodman scored the game's only try just before halftime, New Zealand was forced to hold on after Tyla Nathan-Wong was yellow-carded for a late tackle.
It did so, defending stoutly and scrambling well to cut down space on the outside as the US enjoyed more ball and field position.
New Zealand will meet Great Britain in the semifinals tomorrow, which advanced after beating Fiji 26-7.
On the other side of the draw Australia beat Spain 24-0, bouncing back after a 12-12 draw with the USA in their final pool match. It will face Canada tomorrow, which beat France 15-5.