Winnipeg trailed 4-2 midway through the third period but rallied on goals by Dustin Byfuglien and Alex Burmistrov to force an extra frame.
In overtime, Olli Jokinen corralled the puck after an Islanders turnover at center ice and skated into the left circle where he unleashed a shot that Evgeni Nabokov blocked, but Kane was there to put in the rebound for the game-winner.
Former Islander Al Montoya stopped 21-of-25 shots for the win.
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