Evan Bouchard, Connor Brown and Adam Henrique also scored for the Oilers (1-3-0), who ended a four-game home stand to open the season. Skinner made 27 saves.
"Our best players really came up clutch," Edmonton coach Kris Knoblauch said. "The game-tying goal, Leon makes a play on the wall, McDavid makes a pass and Bouchard scores. And obviously those guys were on the ice again for the game-winning goal.
"We need those guys to make key plays in key moments, and they definitely did tonight.”
Matvei Michkov scored his first two NHL goals, and Morgan Frost had two assists for the Flyers (1-1-1), who will conclude a season-opening four-game road trip at the Seattle Kraken on Thursday. Ersson made 29 saves.
"We had a ton of chances, too, but we just couldn’t put it in," Frost said. "Unfortunately, we don’t get the two points, but I thought we played a great game. So, I think we can keep our heads held high."
Michkov gave the Flyers a 1-0 lead at 4:46 of the first period, stuffing in the puck at the right post for a power-play goal.