Chicago’s Robert Lang scored the game-winner at 9:19 of the third to break a 2-2 tie.
Goalie Dominik Hasek was beaten three times on 27 Chicago shots.
Detroit had won 11 of its last 12 home games against the Blackhawks.
On the power play, Chicago went 0-for-8, while the Red Wings were 0-for-5.
The Blackhawks had beaten the Red Wings, 4-3, in a shoot-out last Friday.
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