Cloe Lacasse and Evelyne Viens scored on a night that might have been a routine group win for Canada before it was thrust into the global spotlight due to a scandal that saw manager Bev Priestman sit out Thursday's (local time) game and two staff members sent home amid allegations of drone use at two New Zealand practices.
Assistant Andy Spence acted as coach, while Priestman, who had removed herself from the game after New Zealand's complaint, watched it from the team hotel.
The full fall-out from the scandal is yet to be known, as Canada Soccer has launched an independent external review into the matter while global football's governing body Fifa has begun disciplinary proceedings.
Joseph Lombardi, one of the staff members sent home, was handed an eight-month suspended jail term and his material was confiscated, a French court said.
New Zealand coach Indiah-Page Riley, meanwhile, said the scandal "lit a fire in our bellies."
Mackenzie Barry shocked the Canadians by opening the scoring with a goal in the 13th minute when she fired home off the underside of the crossbar after Katie Kitching's corner.
But Canada proved too strong for the women's football minnows, whose best Olympic finish was a quarter-final appearance in 2012, and Lacasse levelled in first-half added time, stabbing home from close-range after some exquisite passing.
Viens netted the winner in the 79th minute in front of a sparse crowd at St Etienne's Geoffrey-Guichard Stadium, when she ran on to a pinpoint long pass from Jessie Fleming and fired first-time into the far corner from a tight angle.
France and Colombia were playing in Thursday's late Group A match, while Spain beat Japan 2-1 in their Group C opener.
