Brent Seabrook, Jonathan Toews, Duncan Keith, Andrew Desjardins and Andrew Shaw each scored and Artemi Panarin also had two assists. Corey Crawford made 27 saves for the Hawks (12-8-2), who hold a 2-1-1 mark on their six-game Circus Trip.
The win snapped a six-game winning streak for the Sharks (13-9), who dropped their third straight at home.
Kane helped the Hawks get on the board first with a feed to Brent Seabrook, who sent a slap shot past Martin Jones for a 1-0 lead at 8:39. The Sharks answered on a power-play goal from Brent Burns, who blasted a one-timer from the right faceoff dot from Joel Pavelski. After the goal, the Hawks successfully killed four penalties.
Toews' breakaway goal less than three minutes later gave the Hawks the lead back. Ryan Garbutt sent a pass to Toews, who sent a wrister from the left circle for his eighth goal this season. Keith extended the lead with a wrister of his own at 12:20 of the second period.
San Jose closed the deficit again midway through the third on Patrick Marleau's goal, but, former Shark, Desjardins, scored 67 seconds later on a rebound.
Shaw added an empty-net goal with 42 seconds left.
The Hawks return to the ice against the Anaheim Ducks on Friday at Honda Center.