The Devils were leading 2-1 when Winnipeg's Grant Clitsome notched the equalizer on a power play 13 minutes into the middle frame.
Kane then struck less than 5 minutes later when he got the puck on a breakaway down the middle, sped past two defensemen and avoided a poke check by New Jersey goalie Johan Hedberg for a goal.
Jets goalie Ondrej Pavelec made 24 saves.
Chipotle plans first price increase in 3 years
Putin thinks Obama would save him if he were drowning