Chiasson won a battle at the front of the net and pushed the puck under Hart during a 5-on-3 power-play at 9:36 to increase the lead to 3-1.
"You're going to get a lot of bounces that don't go your way," Hart said. "We got a couple of bounces to go our way at the end."
Atkinson, in his Flyers debut, brought them within 3-2 at 12:17 when he cut to the slot and redirected a Farabee pass.
Miller gave Vancouver a 4-2 lead at 17:07 when he knocked in a loose puck at the post.
Despite the Flyers rallying in the third, the Canucks felt they carried the play for most of the period.
"It was about as good a third period as you can play in a hockey game on the road," Miller said. "I don't think it took the life out of us at all. I thought we did pretty well in the overtime as well, had some good looks, so we're just really happy. I don't think we had a great first period, power play came up big. And then I thought we had an awesome third period."
NOTES: Defensemen Ryan Ellis and Keith Yandle each had two assists in his Flyers debut. Ellis was acquired in a trade with the Nashville Predators on July 17, and Yandle signed a one-year contract July 28. Yandle's second assist was the 500th of his NHL career. He played his 923rd consecutive game, second to Doug Jarvis (964) in NHL history. … Philadelphia forward Max Willman had one shot on goal in 9:30 of ice time in his NHL debut. … Pettersson's goal was his first since March 2. He missed the final 30 games last season with a wrist injury. … It was the Canucks' first game in the United States since March 1, 2020. Last season they were in the Scotia North Division, which consisted of the seven Canada-based teams. ... It was Vancouver's first win in Philadelphia since Nov. 21, 2017. ... Goalie Jaroslav Halak is expected to make his Canucks debut at the Detroit Red Wings on Saturday.