Brandon Saad also scored two goals for Chicago, which has won three of the four games between the teams. One victory was in a shootout.
Sharp has four goals and four assists against the Stars this season. In his last eight games versus Dallas, he has eight goals and seven assists.
The Central Division-leading Blackhawks (22-6-5) reached six goals for the fifth time this season, and second in a row. They defeated Florida 6-2 on Sunday.
Dallas has given up six goals in three different losses.
For the Stars (14-10-5), Antoine Roussel scored a second-period goal to end Chicago goalie Antti Raanta's shutout bid. Roussel was credited with another goal when he deflected Sergei Gonchar's drive into the net with 19 seconds remaining in the game.
Raanta finished with 27 saves for his fourth win.
Chicago dominated the first period, with 14 shots on goal to four for the Stars. The Blackhawks scored barely 2 minutes into the game.
Kostka drove the puck from the top of the right circle toward a crowd in front of Lehtonen. The deflected puck slid toward the right post. Lehtonen smothered the puck with his glove, and the goal light did not go on.
After a video review, referee Kelly Sutherland announced that the puck had crossed the goal line. Kostka had his second goal of the season, in just his third game.
Seconds after the Stars' Dustin Jeffrey sent a close-in attempt wide left, the Blackhawks quickly moved the puck up ice. Kane skated in on a breakaway and beat Lehtonen at 12:05 for his 17th goal and a 2-0 lead.
It could have been worse for the Stars. Chicago had a 5-on-3 advantage for 1:55 midway through the first. Dallas killed both penalties — with Cody Eakin, Alex Goligoski and Jamie Oleksiak on the ice for all but a few seconds.
The Blackhawks went up 3-0 on Saad's first goal 2:46 into the second period. Kostka took a shot from a narrow angle, Dallas couldn't control the rebound and Saad poked the puck in from in front of the net.
Sharp then scored two goals less than 3 minutes apart for a 5-0 lead. His first, on a power play at 8:20, brought Ellis in to replace Lehtonen. Sharp then took a long pass from Duncan Keith at the Dallas blue line and beat both Goligoski and Ellis for his second goal of the game and 14th this season at 11:08.
The period ended 6-1 after Roussel's first goal and Saad's second, at 19:15.
NOTES: Raanta started in goal because Corey Crawford reportedly sustained a groin injury Sunday against Florida. Raanta replaced Crawford in the first period vs. the Panthers and earned a victory. The Blackhawks recalled rookie Kent Simpson from Rockford of the American Hockey League to back up Raanta; Crawford did not travel to Dallas. ... The Stars' power-play woes continued. They failed to score on their five power plays, dropping their home success rate to 1-for-47 (2 per cent). Chicago was 1 for 5 with the man advantage.