Chicago posted its fourth straight win and snapped a seven-game losing streak against Detroit that dated to March 2006.
By earning a point for reaching overtime, the Red Wings clinched their sixth straight Central Division Title. Detroit needs one more point to secure its third consecutive Western Conference title.
Pavel Datsyuk scored in the shootout for Detroit.
Chicago's Nikolai Khabibulin made a season-high 56 saves, and Nikita Alexeev and Bryan Bickell scored in regulation.
Kyle Calder was credited with a power-play goal for Detroit at 9:36 of the third to tie it 2-2. However, it appeared that Robert Lang also might have jammed the loose puck past Khabibulin.
Tomas Holmstrom also scored in regulation for Detroit, which came back from a 2-0 deficit. Chris Osgood made 19 saves.