The first half was an even affair and neither side were able to conjure up many clear chances.
Straight after the break Punt gave New Zealand the lead when she finished from an acute angle but the home side were unable to build on their advantage as Wang delivered two of the best.
The Black Sticks earned a collection of penalty corners with 10 minutes left but were unable to find the silver bullet strike to even the game up.
Wang's ability at penalty corners was a threat throughout the game and she could have added a third with five minutes left but Black Sticks goalkeeper Bianca Russell made a fine save.
New Zealand's next game is against the second-ranked Argentina on Tuesday.
In today's earlier results, Argentina continued their good form with a 5-1 win over Korea, while Australia scraped past Japan 1-0.
China 2 (Mengyu Wang 2) Black Sticks 1 (Anita Punt) Halftime: 0-0