Marcus Kruger's goal amid a scrum in front of the net early in the third proved to be the game winner for the Blackhawks, who have won four straight.
Jimmy Hayes scored for Chicago in the second period, tying the score 1-1.
Valtteri Filppula had given Detroit the lead with a power-play goal in the first period but the Western Conference leading Red Wings could not score on Crawford again, despite outshooting Chicago 32-29.
Jimmy Howard made 27 saves in his first start for Detroit since Feb. 2.
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