Radim Vrbata scored 1:15 into overtime to lift 1.
Mikkel Boedker lit the lamp in regulation for the Coyotes, who extended their season-high point streak to eight games (7-0-1). Mike Smith made 30 saves and has now won a career-high seven straight games.
Phoenix has 67 points and sits two behind first-place San Jose in the Pacific Division standings. The Sharks were idle on Saturday.
"We played hard but we need results," Stars head coach Glen Gulutzan said. "It's a results-based business and we need results. We need to capitalize and we can't make a mistake at the end to give away a point."
The Coyotes took advantage of a Stars turnover early in overtime. Ray Whitney stole the puck behind the Dallas net and found Vrbata open in front. Vrbata made a nice move before beating Lehtonen for the win.
"I was running out of room there and I wanted to make sure I had a lane to shoot and I was able to put it in," Vrbata said.
The Coyotes drew first blood at the 13:31 mark of the first period. Boedker led a 2-on-1 rush down the right wing and his shot from inside the circle got past Lehtonen.
Dallas almost tied the game with over 12 minutes remaining in the middle stanza. A shot from the point was knocked down in front by a high stick and Tomas Vincour put the puck into the back of the net. The refs immediately waved off the goal due to the high stick.
But the Stars managed to get on the board with 7:23 to go. A shot from the point left a rebound in front for Ryder, who batted the puck out of the air and past Smith. The power-play score made it a 1-1 game.
Smith made 10 saves in the third frame, while Lehtonen stopped nine shots.
The Coyotes are 3-0-2 against the Stars this season...Smith came into Saturday's game with a shutout streak of 138 minutes and 49 seconds... Phoenix recalled defenseman Michael Stone and forward Matt Watkins from Portland (AHL). Stone made his NHL debut on Saturday...The Coyotes were without defensemen Rostisalv Klesla (upper body) and Derek Morris (groin/illness)...The Stars played without leading scorer Jamie Benn (leg laceration) and defenseman Sheldon Souray (foot).