Detroit has won four of five games. Jeff Hamilton and Tuomo Ruutu scored for the Blackhawks, who fell to 5-1-3 under new coach Denis Savard. Nikolai Khabibulin made 23 saves Cleary extended his point streak to seven games, and has five goals and four assists in the span.
Detroit forward Tomas Kopecky left with an injury 53 seconds into the third period.
The Red Wings centre was motionless on the ice for a few minutes before being helped to the dressing room by members of the Detroit training staff.
As he approached the Chicago blue line, Kopecky went down and slid into the left boards before Blackhawks defenceman Jim Vandermeer fell on top of him.