Dallas jumped a point in front of San Jose for the top spot in the division after the Sharks dropped a 3-1 decision Wednesday to Anaheim.
The Stars have 89 points in the frantic Western Conference playoff chase, in which six teams began the night separated by three points in the fight for the final three post-season spots.
Ryder opened the scoring midway through the first period and gave Dallas a 3-0 lead early in the third. He also assisted on Mike Ribeiro's second-period goal. Ryder has 35 goals, putting him among the NHL's Top 10 scorers this season.
Kari Lehtonen made 31 saves for the victory, which was only the third in seven games for the Stars.
Edmonton, which is out of playoff contention, got 22 saves from Devan Dubnyk. Ales Hemsky scored the only goal for the Oilers with 11:39 to play in the contest.