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