Canada bombarded the New Zealand goal with 22 total strikes in Grenoble, 11 of them on target. But it wasn't until the 48th minute that they took the lead, Jessie Fleming scoring just after half-time before Nichelle Prince ensured Canada stayed in front.
"We were creating chances and had more shots than against Cameroon, so it was a positive. We just need to find a way through. It was a great performance by the team and I am proud to be their coach," said Kenneth Heiner-Moller.
"We were outplayed all over the field. We never got into any kind of rhythm or into any situation where we won things to get momentum. We were beaten by the better team," concluded New Zealand coach Tom Sermanni.
Canada and the Netherlands meet in Reims on 20 June to decide who will top the group.
At the same time, New Zealand will play Cameroon in Montpellier.
Dutch out in force
Forward Vivianne Miedema registered her 59th and 60th international goals in Valenciennes in the match against Cameroon, becoming the first Dutch player to score more than once in a Women's World Cup match.
"I am 22 years old and I hope I have a nice career in front of me," Miedema told reporters after the match. "I have no idea where this will end, but as long as I continue playing at his level I hope to keep adding more goals."
Her goals came either side of a close-range Dominique Bloodworth strike.
Gabrielle Aboudi Onguene netted for Cameroon.
Sarina Wiegman's team were helped by huge Dutch support, with around 15,000 fans present in the northern French town which lies only a two-hour drive across Belgium from the southern Netherlands.
"The fact that the match was played in Valenciennes which is very close to Holland, I think that put us at a disadvantage," said Cameroon coach Alain Djeumfa, insisting that gave the Dutch a "psychological" edge.
In group F matches on Sunday, Sweden play Thailand, while USA face Chile.