Joel Farabee and Sean Walker scored, and Sean Couturier and Owen Tippett each had two assists for Philadelphia (3-1-0). Carter Hart made 22 saves.
"I thought tonight we checked well," Flyers coach John Tortorella said. "Not only checking but I thought we were clean through the neutral zone. We didn't turn many [pucks] over. You just can't turn it over with that team. Their offensive people don't want to play in their end zone, so we really tried to concentrate on just placing pucks in their end zone and playing there. Getting through the neutral zone clean was a very important part of tonight's game."
Zach Hyman scored for Edmonton, which has lost three of its first four games (1-3-0). Jack Campbell made 28 saves.
"I thought our game lacked urgency today," Oilers coach Jay Woodcroft said. "I didn't see second and third effort in all areas of the game from up and down our lineup. Not to our standard; we play towards a standard and it wasn't there for us tonight and that's disappointing."
Atkinson, who missed last season because of a neck injury, had his first two-goal game since March 5, 2022.
He gave the Flyers a 2-0 lead at 3:54 of the second period, tipping a centering pass from Tippett past Campbell.
Atkinson scored again at 4:17 of the third period to make it 4-1.
"It feels good," Atkinson said. "I love playing at home in front of our fans. Kind of gives me a little bit more motivation, family in town and stuff like that. It's always nice to score goals. That's what I'm here to do."