Chicago moved within reach of a playoff spot, having gone into the evening's action needing a victory over Detroit and a loss by Dallas to wrap up a post-season berth.
Drew Miller tallied for the Red Wings with 22 seconds remaining in the middle period and Tomas Holmstrom scored with 1:20 to go in the third.
The defending Stanley Cup champion Blackhawks will finish their regular season Sunday by hosting Detroit.
Corey Crawford made 26 saves to get the win. Jimmy Howard was beaten for all four Chicago goals on 29 shots.
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