Sharp got all four of his helpers in the second period, when the Blackhawks erased a 2-1 deficit with five goals, including both of Hossa's power-play markers.
Jonathan Toews and Patrick Kane added a goal and an assist each and Corey Crawford stopped 33-of-36 shots for the Hawks, who shelled their former goalie Antti Niemi and moved into fourth place in the Western Conference playoff seeding.
Niemi backstopped Chicago during its Stanley Cup championship run last season and had gone undefeated in three meetings against his former mates this season.
He yielded four goals on 18 shots Monday before being pulled in favor of Antero Niittymaki, who stopped 14-of-16 shots the rest of the way for the Sharks.
Joe Pavelski notched a goal and an assist and Logan Couture and Joe Thornton also found the net for Pacific Division-leading San Jose.