Kane scored his fourth goal against Dallas this season, Cristobal Huet stopped 30 shots and the Chicago Blackhawks completed a season sweep of the Stars with a 3-1 victory on Saturday.
Defensemen Matt Walker and James Wisniewski also scored for the Blackhawks, who outscored the Stars 20-8 in their four meetings this season.
The Blackhawks were 6-2 winners a week ago in Chicago in the teams' previous matchup.
"We knew it was going to be a tough game and not as easy as the last time against them," Kane said. "To get a win here is pretty big."
Kane also had four assists against Dallas this season. He said the Stars' physical play brings out the best in him.
"I think when you get hit a lot, it kind of gets you in the game and makes you try to create more plays," he said.
Huet, making his fifth straight start while Nikolai Khabibulin is out with a lower-body injury, denied Jere Lehtinen on a first-period breakaway to keep the game scoreless. He also made a tough save against Fabian Brunnstrom from close range with 3:10 remaining.
Huet seemed headed for his second straight shutout and 21st of his career before Steve Ott scored on a breakaway with 8:29 left during a delayed Chicago penalty.
The Blackhawks wrapped up a stretch of 11 road games in a 12-game span, going 8-3 in the 11 road contests to improve to 19-11-3 away from the United Center. They have eight of their next 10 at home starting Sunday against Minnesota.
Chicago lost two in a row at home before the 11-of-12 road swing, and Wisniewski said being on the road for so long actually helped the Blackhawks regain their focus.
"I think the road trip was the best thing for us," Wisniewski said. "We got back to playing playoff hockey, Chicago Blackhawk, high-intensity hockey. Just getting in there, flying around, buzzing around, and getting pucks on net, not being too pretty, too cute."
Marty Turco had 33 saves for the Stars, playing their second game since losing No. 2 scorer Brad Richards to a broken wrist. Richards, who had been among the team's best players after starting the season slowly, could miss eight weeks after he was injured in Monday night's 3-2 shootout victory at Columbus.
"You can't take a player like that out and not feel it," Stars coach Dave Tippett said.
The Stars were 10-3 in their previous 13 games, but they continued their futility against the Blackhawks and missed an opportunity to gain ground in a tight race for one of the bottom four Western Conference playoff spots.
"Every year you have one team who you can't get points against," Stars defenseman Darryl Sydor said. "It's frustrating. But you have to swallow that pill and move on."
Tippett said the Stars needed a better effort to keep pace with the young, talented Blackhawks.
"They played a good game but in our situation we have little room for error," Tippett said. "If you have five, six guys not pulling their weight, that's a problem. We looked like a tired, frustrated team chasing the game. We can't have any weak links."
Wisniewski, who turned 25 on Saturday, scored his second of the season to put Chicago ahead at 16:04 of the opening period. With the Blackhawks on a power play, he converted a one-timer from beyond the right circle.
Dallas got a break at 5:46 of the second when Kris Versteeg's attempt from the slot rang off the post.
Kane didn't miss at 7:23, firing a sharp-angled shot past Turco for his 19th of the season.
Walker's deflection with 16 seconds remaining in the second was his first goal of the season, bumping Chicago's lead to 3-0.
"We've got some guys [on defense] who can hit the puck pretty hard and sometimes they go in," Blackhawks coach Joel Quenneville said.
Huet improved to 17-10-3. He's shared the goaltending load with Khabibulin, who was 17-5-5 before his injury. ... Turco was making his 29th consecutive start. ... Wisniewski has four points in his last four games.
Copyright by STATS LLC and The Associated Press
Arena: American Airlines Center Location: Dallas, Texas
Referees: Dave Jackson, Tom Kowal Linesmen: Brad Lazarowich, Andy McElman
Attendance: 18,584 (100.3% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
James Wisniewski (2)
(Power Play) Assists: Martin Havlat, Kris Versteeg
Patrick Kane (19)
Assists: Troy Brouwer, Jonathan Toews
Matt Walker (1)
Assists: Cam Barker, Dustin Byfuglien
Steve Ott (12)
Assists: Trevor Daley, Stephane Robidas