San Jose used three power-play tallies and a shorthanded goal to improve to 1-4-0 on its seven-game road trip, which concludes with games against Dallas and Los Angeles.
With the score tied at 2-2, Blackhawks defenseman Phil Housley clipped All-Star Teemu Selanne and received a high-sticking penalty with 6:46 remaining. Teammate Nathan Dempsey was penalized for goaltender interference 57 seconds later, giving the Sharks a two-man advantage.
Facing the NHL's best home penalty-killing unit, San Jose needed just 34 seconds to take the lead as Patrick Marleau slid a pass across the crease to Damphousse, who lifted the puck over goalie Jocelyn Thibault for his 15th goal.
Less than a minute later, Mike Ricci centered from behind the net to Thornton, who wristed a shot from the left faceoff circle under the crossbar for his ninth goal.
Miikka Kiprusoff stopped 23 shots for the Sharks, who defeated the Blackhawks for just the second time in the last seven meetings (2-3-2).