The Blackhawks, despite letting an early two-goal lead slip away, boosted their point total to a league-high 72. The Red Wings have lost in a shootout in each of their last two games and remained one spot out of a playoff position in the Western Conference.
Both sides scored in the first and third shootout rounds before Sharp lifted the puck past Jimmy Howard and just under the crossbar.
Sharp also scored in regulation, as did Troy Brouwer and Patrick Kane. Chicago won for the seventh time in nine games.
Backup goaltender Antti Niemi made 35 saves for the win, his 11th in 15 decisions this season. Howard stopped 26 shots.
Chicago has defeated Detroit in three of their four contests. The Blackhawks had shut out the Red Wings in their previous two meetings.