The Dutch went ahead early in the second quarter when Rob Kamperman's through ball eluded final defender Blair Tarrant, and Jeroen Hertzberger went around goalkeeper Devon Manchester to expertly score with a reverse shot.
New Zealand stepped up in the second spell, had more circle penetrations and shots on goal than the Dutch, who seemed to lose their rhythm.
Hilton was unsighted when the impressive Arun Panchia's drive across from the right eluded two defenders, and could not react in time to a fine chance.
It was a game of no penalty corners until right at the death when Tarrant won a chance with an incisive run along the goal line from the left.
Haig stepped up and drilled the ball low and hard past goalkeeper Pirmin Blaak's right hand.
There was even a late opportunity for the Black Sticks to win the match when they were awarded a contentious second penalty corner with 10s left. However Andy Hayward's drive was deflected high over the goal.
''I think we got what we deserved, considering all the effort the boys put in in the second half," Haig said after the match.
''We were a little disappointing in the first half, we weren't so clinical up front but we put a lot of pressure on in the second half and created good attacking opportunities."
Hertzberger acknowledged the result was a fair one.
''New Zealand is a good team and showed that today. They kept on going and if we are honest they deserved it. But it's very disappointing for us."