Lehtonen made 30 saves, Jamie Benn and Adam Burish each had a goal and an assist and the Stars beat the Oilers 4-2 on Thursday night.
"Kari was very good tonight, especially when we needed him to be," Stars coach Marc Crawford said. "We weren't very good in the first period tonight and the Oilers were. They had a number of chances and he was equal to the task."
Mike Ribeiro and James Neal also scored for Dallas. The Pacific Division-leading Stars have won a team-record eight straight road games and are 7-0-1 in January and 29-13-5 overall.
"It starts with goaltending," Ribeiro said. "Both of our goaltenders have been amazing. It's every guy on the team right now as well. It's coming from everywhere."
Former Michigan State defenseman Jeff Petry scored his first NHL goal, and Ryan Jones added a goal for Edmonton. The Oilers, last in the Western Conference at 14-25-7, have lost four in a row and 13 of 15.
"We went to the net hard and put pucks there and did lots of things that you need to do to have success," Oilers coach Tom Renney said. "But we turned the puck over enough times and that helped their attack."
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Edmonton goalie Nikolai Khabibulin suffered his 10th straight loss.
Dallas opened the scoring 12 minutes into the first period as Burish chipped the puck off the boards to send Benn on a breakaway. He beat Khabibulin with a nifty deke for his 13th goal of the season.
The Oilers scored short-handed just over a minute later when Jones converted Kari Lehtonen's rebound.
The Stars regained the lead 6½ minutes into the second. Ribeiro sent the puck back to a trailing Niklas Grossman, who gave it right back to Ribeiro at the side of the net for his 10th goal.
Dallas made it 3-1 on a power play midway through the second. Benn got past Edmonton's Colin Fraser and passed to Neal, who picked the top corner for his 19th goal of the season.
Petry scored late in the second with a blast from the point.
"It's a special day. Obviously it would have been better with a win, but it was a pretty good goal to get," Petry said. "I didn't see it. I didn't see the light go on either. I saw everybody stand up behind the net, though."
NOTES: Burish scored into a empty net with a second left. ... It was the second of four meetings between the teams this season. The Stars won the first game 3-2 on Jan. 11. ... Edmonton was without forward Ales Hemsky (concussion), but captain Shawn Horcoff returned from a knee injury.