Kane assisted on goals by defensemen Cam Barker and Brent Sopel. Andrew Ladd and Dustin Byfuglien also scored for Chicago, which remained unbeaten in regulation at home (4-0-2).
Loui Eriksson and Steve Ott scored for Dallas, which opened a five-game road trip.
Chicago's Nikolai Khabibulin made 21 saves.
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Dallas backup goalie Tobias Stephan stopped 27 shots in his second straight start in place of struggling Marty Turco. Stephan earned his first NHL victory on Wednesday, 4-2 over Minnesota. Friday's start was only his second this season and third in the NHL.
The Stars entered the game with an NHL-worst 3.95 team goals-against average. Turco has a 4.26 goals-against and .842 save percentage. Stephan's start
Eriksson opened the scoring 6:17 in, scoring from the right edge of the crease after taking Brenden Morrow's cross-ice feed.
Barker's power-play goal midway through the first tied it at 1. Barker, playing his second game since being recalled from Rockford of the AHL on Monday, connected on a screened drive from the top of the slot.
Kane put Chicago ahead 2-1 with 1:10 left in the first when he took a pass from Martin Havlat to complete a 2-on-1 break.
Ott tied it 2-all at 7:39 of the second on a breakaway from center ice.
Sopel restored Chicago's lead 3-2 with 6:34 left in the second. Left uncovered at the right point, Sopel took Kane's pass from the left boards, skated to the top the circle and ripped a high shot that clanked in off the left post.
Ladd and Byfuglien each scored their first goals of the season late in the third to seal Chicago's victory.
Ladd scored on a 2-on-1 with 6:10 left in the third to make it 4-2. Byfuglien made it 5-2 just over two minutes later when he connected from the edge of the crease.
Notes:@ Dallas C Brad Richards missed the game with a lower-body injury. The Stars did not disclose how long Richards might be out. Dallas RW Jere Lehtinen missed his 11th game with a groin injury and D Doug Janik missed his sixth straight with an eye injury. Both are day to day and could return within a week. Stars D Sergei Zubov, who has not played this season due to hip injury, is expected to return next Friday at Anaheim. ... Chicago D Niklas Hjalmarsson missed his seventh game with bruised ribs. ... Sopel's goal was his first since Jan. 11, 2008. ... Stephan made his first NHL start against the Blackhawks last season, stopping 38 of 40 shots in a 2-1 overtime loss on Oct. 13, 2007.