The Black Ferns will take the 40-22 win over Canada, but they know there is much to do to take down England in their next match of the women's Super Series on Thursday.
In warm conditions in Calgary, the Black Ferns scored seven tries to four in an open clash, but they were pressured in the opening quarter and in the scrums by a committed Canadian outfit.
The score might have been much higher were it not for No 9 Kendra Cocksedge kicking only two from seven off the tee, though she played very well around the field and took the official player of the match gong.
Black Ferns debutant blindside flanker Charlene Halapua opened the scoring after just five minutes on the short side, before wing Honey Hireme swung into action, showing her sheer pace for an impressive brace.
Second five Chelsea Alley was also prominent, making several thrusts in the midfield and scoring a try of her own.
Turning at 18-12, New Zealand were quickly into their second spell work, wing Renee Wickliffe and Victoria Subritzky-Nafatali scoring, but they could not pull clear until triple international Janna Vaughan scored with her first touch of the ball on debut.
Captain and hooker Fiao'o Fa'amausili was proud of her charges.
"Canada gave it to us in the first 20 minutes, especially, but we dug deep in these hot conditions."
They performed well at the breakdown, if not always at the set-piece.
"We take pride in our breakdown and muscling up," she added.
Canada's standout player was openside flanker Latoya Blackwood, who scored a try and muscled up without the ball, making a nuisance of herself in the forward exchanges.
In the first match of the doubleheader, Rugby World Cup holders England beat USA 39-13.
New Zealand faces England in Red Deer in their second game.
Black Ferns 40 (Honey Hireme 2, Charlene Halapua, Chelsea Alley, Renee Wickliffe Victoria Subritzky-Nafatali, Janna Vaughan tries; Kendra Cocksedge con, pen)
Canada 22 (Olivia DeMerchant, Amanda Thornborough, Latoya Blackwood, Tyson Beukeboom tries; Andrea Burk con) Halftime: 18-12 Black Ferns