Kane's one-timer off a pass from Viktor Stalberg with 2:02 remaining in the third period pulled the Blackhawks into a 1-1 tie.
After a scoreless overtime, he notched the only goal of the ensuing shootout while Corey Crawford made a pair of saves, enabling the Blackhawks to remain without a regulation loss in 22 games to start the season -- extending an NHL record.
Crawford turned aside 32-of-33 shots en route to the victory.
Tomas Tatar scored and Jimmy Howard made 32 saves for the Red Wings, who fell for the second time in three contests.
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