New Zealand is now winless in each of its 14 Women's World Cup matches, drawing three and losing the other 11.
Canada secured their place in the last-16 of the Women's World Cup with a 2-0 win over New Zealand.
In the second, Canada played more direct and Fleming's goal came after a ball was played over the top of the New Zealand back line for Prince to chase.
Fleming scored three minutes into the second half to give Canada the lead, turning in a cross from Prince, who added the second just over a half hour later. A probing long ball found Prince down the left flank and the speedy forward outraced two defenders before squaring the ball for the 21-year-old Fleming to slot in her ninth goal in 68 appearances - and first at the World Cup.
Prince came close in the 71st minute when she got to a cross by Sinclair and headed it toward the top corner of the net, but Nayler made an outstanding diving save.
Canada will face the Netherlands in the team's final group match Thursday in Reims, France.
New Zealand goalkeeper Erin Nayler kept the Football Ferns in the contest, twice coming to the rescue to deny Prince, the second a stunning effort to tip over the bar from a header.
Canada is fifth in the current Federation Internationale de Football Association world rankings, 14 spots ahead of New Zealand. A draw won't, however, won't knock New Zealand out of the competition.
Canada came out with objective in the second half, with a 14-pass sequence off the kickoff that led to a Beckie shot over the bar.
Defender CJ Bott picked up a hand injury when the ball hit her, and with the Female Ferns down to 10 players, Canada nearly snatched the lead from a corner.
Canada sits tied with the Netherlands (both on six points) for first place in Group E, although the Dutch hold the tiebreaker because they've scored more goals. "Players from the bench are contributing and the team are getting better", Canada manager Kenneth Heiner-Moller said. It was a great performance by the team and I am proud to be their coach. After the Canadians struggled to break down two ultra-defensive sides, it'll be interesting to see if they can open things up a bit more in the attacking end against the Dutch.
Sinclair remains on 181 goals for Canada, just three away from tying retired USA star Abby Wambach as the all-time leading scorer in the history of worldwide women's soccer.
Canada, hosts four years ago, opened the tournament with a 1-0 win over Cameroon in Montpellier and went close to taking the lead in the 18th minute against New Zealand, who were temporarily reduced to 10 players after CJ Bott had to leave the field with a hand injury.
The world No 19 Ferns were second best from the off against world No 5 Canada, who finished with 70 per cent of possession and had 22 shots to the Ferns' two, but centre backs Abby Erceg and Rebekah Stott ensured there weren't a lot of clear-cut chances on offer. "We dominated but just weren't able to put one in", said Sinclair.