Leighton made 31 saves and Dallas' Marty Turco stopped 29 shots in the 1-1 tie Sunday night.
"I want to eliminate the soft goals and make them work for their goals," Leighton said. "If I do come up with a good save, it's a bonus."
Steve Sullivan opened the scoring for the Blackhawks in the first period, and Dallas' Sergei Zubov tied it in the second with a short-handed goal.
"Leights was outstanding," Chicago coach Brian Sutter said.
He also got some big breaks.
Dallas' Bill Guerin missed on a short-handed two-on-one break with Mike Modano five minutes into the third. Guerin fired Modano's pass just wide of the post and off the net.
Jason Arnott nearly gave Dallas a 2-1 lead in third on a breakaway after leaving the penalty box.
Arnott lofted a point-blank backhand shot that beat Leighton, but bounced down off the crossbar, along the goal line, off the right post and into the slot. The loose puck was cleared by Chicago defenseman Stephane Robidas.
"I knew it hit the crossbar," Arnott said. "I didn't know if it his the crossed the line when it came down. Unfortunate bounce, it didn't cross the line."
With 5:10 left, Leighton made a point-blank save on Guerin during a Dallas power play. Guerin's stick broke on the play.
The Blackhawks, 1-10-3-3 in their last 17 games, have 12 goals in their last seven contests.
The Stars are 1-5-1 in their last seven, scoring just five goals during that span. Dallas has not scored more than one goal in any of those contests.
"We need scoring," Stars coach Dave Tippett. "We can say, "Oh let's just hang in there, it will come.' But you know what? Confidence is earned. Someone's got to take responsibility and bury one of those chances."
Sullivan opened the scoring midway through the first period, completing a partial breakaway.
After taking Brett McLean's feed at the blue line, Sullivan streaked down the slot. While making a move, he appeared to lose control of the puck, but it slid under Turco's pad.
Zubov's tied midway through the second period with a short-handed goal that capped a three-on-one1 break.
Zubov, Brenden Morrow and Rob DiMaio's broke down the ice with only Sullivan back. Morrow, DiMaio and Zubov finished a passing play that culiminated with Zubov scoring from the left circle.
|Steve Sullivan (5) ASST: Brett McLean (9), Michael Leighton (1)|
1 - 0 CHI
|SHG - Sergei Zubov (3) ASST: Rob DiMaio (5), Brenden Morrow (13)|
1 - 1 Tie
|Ryan Vandenbussche Fighting against Gavin Morgan|
|Gavin Morgan Fighting against Ryan Vandenbussche|
|Larry (Burke) Henry Interference against Scott Young|
|Steve Poapst Holding against Stu Barnes|
|Igor Radulov Hooking against Mike Modano|
|Jon Klemm Interference|
|Scott Nichol Boarding against Scott Young|
|Nathan Dempsey Tripping|
|Stu Barnes Interference against Scott Nichol|
|Steve Sullivan Roughing against Niko Kapanen|
|Niko Kapanen Roughing against Steve Sullivan|
|Jon Klemm Tripping against Tyler Arnason|
|Jason Arnott Hooking against Deron Quint|
|Kyle Calder Too many men on the ice|