Jordan Eberle had a goal and an assist and Taylor Hall also scored for the Oilers (24-30-6), who have the second-worst record in the NHL.
The Flyers (33-20-7) missed a chance to pull into second place in the Eastern Conference.
Edmonton broke the deadlock on a power play at 3:26 of the second. Hall was able to find an inch to squeeze the puck between the post and Ilya Bryzgalov's skate for his 22nd of the season and a 1-0 Oilers lead.
Edmonton went up 2-0 at 8:04 of the second as Eberle picked up a loose puck and sent a shot from the slot that bounced off Bryzgalov's inside pad before trickling across the goal line.
It was the 27th goal and 60th point this season for the second-year forward.
Late in the period, the Flyers' Scott Hartnell was given a kneeing penalty after taking a run at Magnus Paajarvi who had to be helped off the ice with what looked like a knee injury.
Edmonton outshot Philadelphia 15-6 in the second period.
The Flyers came close to scoring five minutes into the third as a Jakub Voracek shot got past Dubnyk, but was fished to safety by Oilers defender Tom Gilbert before it crossed the goal line.
The Oilers were awarded a penalty shot with just under three minutes to play as Kimmo Timonen hauled down Shawn Horcoff on a short-handed breakaway.
Horcoff was stopped on the chance.
It was Dubnyk's third career shutout.
The highlight of the scoreless first period was a marathon fight between the Oilers' Darcy Hordichuk and Philadelphia's Jody Shelley eight minutes into the game.
The Flyers had 14 shots on Dubnyk to Edmonton's nine on Bryzgalov in the first.
However, the Oilers had the best chance of the opening period as Hall made a nice backhand feed from behind the net to Ales Hemsky, but Bryzgalov came across his crease quickly to make the stop.
Notes: It was the only meeting between the two teams this season. ... Oilers coach Tom Renney missed his fifth game with a concussion after taking a puck in the head in practice. Associate coach Ralph Krueger has been guiding the team. ... The Oilers were still without rookie sensation Ryan Nugent-Hopkins, but he has started practicing with contact and could return from a shoulder injury as soon as Saturday. ... Besides the long-term injuries to forward Tom Sestito (groin) and defenseman Chris Pronger, the Flyers fielded a healthy team. ... Both teams have been strong on the power play this season as the Oilers came into the game fourth and the Flyers ranked fifth in the league. ... Flyers forward Jaromir Jagr still needs just one point to move into eighth place in NHL scoring. He is tied with Joe Sakic with 1,641 points.