It keeps them in the running for a last-four place heading into Monday's final fixture against Germany, who are also chasing a semi-final place.
Kayla Sharland converted a penalty corner inside two minutes but the USA equalised when Paige Selenski provided the pass for Katie O'Donnell to score.
Gemma Flynn volleyed home a ball bouncing around the circle after Sharland and Stacey Michelsen had been involved in the build-up to put New Zealand ahead again, only for Claire Laubach to level from a deflected penalty corner just before half-time.
The second half was equally as open and New Zealand had a third goal disallowed by the video referee when Michelsen's reverse-stick shot was turned in by Katie Glynn with a stick over shoulder height.
But Clarissa Eshuis' dipping penalty corner flick beat goalkeeper Amy Swensen with six minutes to go to end the USA's interest.