It was pretty even from then on. It was not until nine minutes from the end that Tom Craig increased the lead with an overhead deflection.
Striker Hugo Inglis closed the gap with a goal from a sharp angle five minutes from the end before Glenn Turner's late goal regained the two-goal margin.
Nick Wilson and Ryan Archibald both went close for the Black Sticks, who felt it had been a good hit out.
New Zealand certainly held some cards up their sleeve ahead of Sunday's match but believed they had gained much from the match.
Fiji thumped Samoa 20-0 in the other men's game, while Australia's women belted their Samoan opponents 25-0.
The women's Black Sticks, ranked fourth in the world, had a day off today as they prepare for back-to-back games against second-ranked Australia on Saturday and Sunday. Both those sides have qualified for Rio, so their matches will be more about pride than absolute necessity.