With the Dallas getting outplayed by Edmonton in the first half of the game, Shawn Horcoff credited Kari Lehtonen for giving the Stars a chance to get going.
Lehtonen stopped 22 shots for his 23rd career shutout as the Stars beat the struggling Oilers 3-0 on Wednesday night.
"He's one of the best in the league and he gives us a chance to win like that every night," Horcoff said.
Rich Peverley, Antoine Roussel and Tyler Seguin scored for Dallas, which has won four of its last five games.
The Oilers controlled the play in the scoreless first period, outshooting the Stars 11-9, and continued to squander power-play chances, including a lengthy 5-on-3 early in the second. Peverley then got Dallas on the scoreboard with 9:15 left in the second period when he knocked in a rebound of his own shot for his fourth goal of the season.
Seguin and Roussel had empty-netters 38 seconds apart in the final minute to seal the Stars' win.
"I think in the first, we started real slow and we gave up...