Kane's short-handed goal at 15:43 of the second period staked the Jets to a 3-1 lead that stood up behind a solid night in the nets by Ondrej Pavelec, who stopped 40-of-42 shots.
The defeat was the first regulation loss of the season for the Ducks, who slipped to 20-1-2 on their home ice.
Anaheim goaltender Jonas Hiller allowed two goals on 11 shots before being replaced by Frederik Andersen, who made 10 saves.
Cam Fowler put the Ducks ahead 1-0 with a power-play goal in the first period. Nick Bonino scored on a rebound at 10:18 of the third period to cut Winnipeg's lead to 3-2.