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.
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