Patrick Sharp, Jeremy Morin and Troy Brouwer each had a goal for the Blackhawks, who have won five of six. Corey Crawford stopped 28 shots in the win.
James Neal and Loui Eriksson each had a goal and an assist for the Stars, who have dropped two straight on the heels of a six-game winning streak. Brandon Segal lit the lamp and Andrew Raycroft stopped 20-of-24 shots in the loss.
"I think the second period hurt us," Stars forward Adam Burish said. "We made it competitive at the end and I think we can feel good about that."
Chicago opened up the scoring 3:18 in on a delayed penalty call when Bickell ripped the puck into the back of the net on a wrister from the high slot.
Just over 10 minutes later, the Blackhawks made it a 2-0 game as Toews' shot from the outside right circle went past Raycroft as two players crashed the net.
Just 1:36 into the second, Chicago took a 3-0 lead on a 3-on-2 break as Dave Bolland sent the puck from the right circle to the slot where Morin wristed it home for the first goal of his NHL career.
Dallas got one back just 20 seconds later when Neal snuck a backhand past Crawford, but Chicago answered just 25 seconds later on Brouwer's sixth goal of the season.
However, the Stars scored with 3:54 left in the second on Segal's fourth goal of the season and Eriksson made it a 4-3 game just 1:05 later when he stuffed the puck in from the low right side for his 11th goal of the season.
Dallas had an early power play in the third, but allowed two Chicago power plays in the latter stages of the game and, with Chicago on the advantage and Raycroft pulled, Sharp scored into the empty net just moments before time expired.
"This has been a trend around here for at least a year or two. We get up by three or four and we lose our concentration," Blackhawks head coach Joel Quenneville said. "We were better in the third period and we had to be."
Before the game, Chicago placed winger Marian Hossa on injured reserve with a lower body injury. He has been out since colliding with teammate Nick Boynton during a November 29 practice...Dallas recalled goaltender Richard Bachman as regular goaltender Kari Lehtonen experienced lower-body stiffness prior to the game. Also, the team activated defenseman Mark Fistric from injured reserve and assigned him to Texas for conditioning. Fistric has missed the last seven games with a lower-body injury...Chicago goaltender Marty Turco, who left Dallas in the past offseason as the franchise's all-time leader in wins and shutouts, did not make an appearance in the game.