Canada dominated the first half and Fleming put them ahead three minutes after the interval following a fine run by Prince who cut the ball back for her team mate to score from eight metres.
Prince grabbed the second goal after 79 minutes, stabbing home from close range after Christine Sinclair's header struck the post.
"It is a great team, I can trust the players. Players from the bench are contributing and the team are getting better," Canada manager Kenneth Heiner-Moller said.
New Zealand have lost their opening two matches and look set to exit the tournament at the group stage.
