Hyejin Cho equalised when unmarked at the far post in the 51st minute, and Seunga Park got the winner with a spectacular reverse stick shot after a long ball forward had eluded two defenders.
New Zealand had 57 percent possession and a 12-7 shot advantage but lacked the finishing class.
Co-captain Stacey Michelsen, who had some fine individual moments, was critical of New Zealand's defence.
"Our marking, and knowing where their players were, was terrible. We need to rectify that and there was a lack of discipline on our part," she said.
However at the other end of the pitch, the failure to grab more than one of many openings cost the Black Sticks dearly.
Olympic champions England's ambitions to lift the trophy took an early dent today.
They went down 2-0 to a committed Germany, both goals coming in the final nine minutes, and both from penalty corners.
There wasn't much in the statistics, although one key number had Germany with eight penalty corner chances to three for England.
The Olympic bronze medallists in Rio last year got the win through quality strikes by Charlotte Stapenhorst and Nike Lorenz.
World No 3 and defending title holders Argentina were far too good for eighth-ranked China, winning 3-0 in blustery conditions with goals from Noel Barrionuevo, Martina Cavallero and Maria Granatto.
They restricted China to just one circle entry in the match and no shots on goal.
World No 1 the Netherlands made it two wins from as many games with a convincing 2-0 win over the US in driving rain tonight, both goals coming from impressive attacker Maartje Krekelaar in the 18th and 37th minutes.
The Dutch dominated the match. They had 22 shots on goal to three by the world No 7 US; 30 to four circle penetrations and a 70-30 possession advantage.
Points after two days:
Pool A: Netherlands 6, Korea 4, US 1, New Zealand 0.
Pool B: Argentina 3, Germany 3, England 0, China 0.