Cameron Barker finished with a goal and an assist for Chicago, which snapped a two-game skid. Brent Sopel, Andrew Ladd and Dustin Byfuglien each tallied in the win for the Blackhawks.
Nikolai Khabibulin stopped 21-of-23 shots for Chicago, including all 10 he saw in the third period.
Loui Eriksson and Steve Ott each scored for Dallas, which played without center Brad Richards, who was scratched with a lower body injury.
Tobias Stephan made 27 saves in the loss for the Stars, who have not recorded back-to-back wins this season.
With the game tied in the middle of the second period, Sopel gave the Blackhawks the lead. A pass from Kane from the left side of the ice went to the top of the right circle for Sopel, whose blast from there beat Stephan for a 3-2 Chicago edge with 6:34 left in the period.
The Blackhawks maintained that advantage well into the third period, then added a pair of insurance goals. A Dallas turnover in the Chicago end led to a 2-on-1 rush for the Blackhawks. Ladd got to the puck first on the left side of the ice and had a clear lane to shoot, as the lone Stars defender was forced to stay in the slot to protect against a cross-ice pass.
Ladd then snapped a shot over Stephan with 6:10 remaining for a 4-2 Blackhawks lead. Byfuglien tallied with 4:09 remaining to increase Chicago's lead to three.
Eriksson scored the game's opening goal at the 6:17 mark of the first period, but Barker evened the contest with a power-play goal at the midway point of the stanza.
Kane's goal with 1:10 left in the first gave Chicago a 2-1 edge, but Ott netted the equalizer at 7:39 of the second.