The Blues went on a man-advantage with 3:26 left in a 1-1 tie game after Dustin Byfuglien was whistled for hooking.
Shattenkirk got the puck in the high slot 26 seconds later and launched a shot that changed direction after hitting the stick of the Jets' Bryan Little. It knuckled past Ondrej Pavelec for the decisive score.
Little scored and Pavelec finished with 18 stops for Winnipeg.
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