Benn Ferriero's goal early in the third period 3 victory at HP Pavilion.
Antti Niemi stopped 30-of-33 shots for the win.
"We have got to find ways to be a little more consistent," Sharks head coach Todd McLellan said. "You could see the desperation in both teams, which are good games to play in, especially when we're winning."
Corey Crawford allowed all five goals on 27 shots to take the loss.
San Jose held a 3-2 lead entering the third period, but Dave Bolland slid a pass from the left corner to the right circle through the legs of a Sharks defender that was one-timed home by Bickell to knot the game at three 2:15 into the final stanza.
Ferriero then put San Jose back on top at the 5:40 mark when he finished off an offensive flurry with a quick shot from the crease that snuck by Crawford.
McGinn gave the Sharks a little insurance with 5:56 left in regulation while on the power play by grabbing a pass to the right of the net before moving the puck from his backhand to his forehand and lifting a shot over the goaltender's right shoulder.
"We know we can win hockey games. We have got a good team, but we just have to get our confidence back," Blackhawks forward Marian Hossa said. "We have to play a team game. We win as a team and we lose as a team."
A pair of power-play goals by Braun and Boyle in the first period sent the Sharks into the first intermission with a 2-0 lead.
The Blackhawks, though, battled back to tie the game when Kruger was able to clean up a pair of rebounds early in the second period.
But San Jose took a 3-2 advantage into the end of the second thanks to a fortuitous deflection.
After the Sharks' Patrick Marleau failed to get the handle on a cross-ice pass in a 2-on-1 rush, Thornton attempted a centering pass from the right of the net that deflected off the stick of San Jose's Dylan Olsen and slid through the legs of Crawford.
San Jose improved to 18-9-2 at home this season, while Chicago fell to 10-13-3 on the road...The teams split the four-game season series 2-2...Brent Burns had three assists and Logan Couture had two helpers for the Sharks...Patrick Sharp recorded two assists for Chicago...San Jose went 3-for-6 on the power play...The Blackhawks failed to score on their three man advantages.