Kris Versteeg had a goal and two assists, while Brian Campbell and Ben Eager each scored and had a helper for the Blackhawks, who opened the swing with a 3-2 shootout win at Phoenix on Tuesday. They still have games against Toronto, San Jose, Anaheim and Los Angeles before returning to the United Center on Dec. 3.
Nikolai Khabibulin made 31 saves for the Blackhawks, winners in six of their last nine overall. They also won at Dallas for just the second time in the last 12 encounters.
Mike Modano, Brenden Morrow and James Neal had the goals for the Stars, losers in four of their last five games. Marty Turco made 24 saves in defeat.
Campbell gave the Blackhawks a 3-2 advantage at 9:08 of the middle period, but Neal tied the game again with a rebound tally with 3:54 remaining in the frame.
Versteeg then boosted Chicago to the lead again with 30 seconds remaining in the period on a tremendous individual effort. He skated with the puck through the left circle before veering in front, and while falling down got the puck past Turco.
Martin Havlat made it a two-goal difference at 6:40 of the third with a successful wrist shot from the right circle and Kane added an empty-net tally in the last minute.
Morrow scored on a rebound of a Mark Parrish shot 7:37 into the contest, but Kane tied the game with 37 seconds remaining in the stanza on a wrister from the top of the left circle.
Eager gave Chicago a 2-1 edge at 6:44 of the second as his snap shot squeaked between the pads of Turco, but Modano lit the lamp 66 seconds later on the power play on a shot from above the left circle.