With Philadelphia's Darroll Powe in the penalty box, Sam Gagner sent a backhand pass to the hard-driving Potulny. The former Flyers forward shoveled his 12th of the season past goalie Michael Leighton.
Jeff Deslauriers stopped 33 shots to earn his second shutout of the season.
The Oilers have won both of their games in February after going all of January without a victory. Edmonton, which has only three wins in 23 games, broke an 0-11-2 slide with a 4-2 home win over the Carolina Hurricanes on Monday night.
The Oilers have an NHL-low 42 points.
Leighton made 26 saves for the Flyers, who had a two-game winning streak snapped.
The Flyers came close to scoring midway through the first period. Danny Briere stole the puck from defenseman Denis Grebeshkov in front, but was stopped in tight by Deslauriers. With 4 minutes left in the period, Mike Richards' shot at a wide-open net sailed through the crease. The Flyers captain to look skyward in disbelief.
Philadelphia had 14 shots in the first, and Edmonton recorded 11.
The Flyers continued to dominate the quality chances in the second, particularly on a power play with 6 minutes left. Deslauriers caught a break with just over a minute remaining when Lukas Krajicek hit the post.
Ethan Moreau's shot to give Edmonton the lead with 6 minutes left in the game deflected off a leg.
Oilers defenseman Alex Plante, playing in his second NHL game, put a puck into the stands with 5 minutes to go but Edmonton killed the penalty for delay of game.
NOTES: The Flyers last beat Edmonton on March 19, 2001. The Oilers have six wins and a tie in the last seven meetings. ... The Oilers hadn't won back-to-back games since a five-game winning streak from Dec. 3-11. ... Edmonton D Sheldon Souray had surgery on Tuesday to repair a broken hand. ... Krajicek played in his second game since joining the Flyers as a free agent. He was brought in to help because defensemen Ryan Parent (back) and Danny Syvret (shoulder) are injured. ... Leighton played in place of Ray Emery, who had started eight consecutive games since returning from abdominal surgery. Emery, who was scratched, has never faced the Oilers. ... Philadelphia LW Daniel Carcillo played in his 200th NHL game.
