Tomas Tatar also had a goal. Howard made 23 saves through overtime, and stopped all three Flyers in the shootout.
Sean Couturier and Claude Giroux scored for the Flyers (6-6-2), Jakub Voracek had two assists and Mason made 33 saves.
The Flyers took a 2-1 lead at 6:51 of the third on Couturier's first goal in 11 games, but Athanasiou tied the game at 11:11 of the third. He got the puck at center ice, showcased his blazing speed when he split Flyers defensemen Brandon Manning and Radko Gudas to break in alone on Mason.
It was Athanasiou's fourth goal in four career games against the Flyers.
"Sometimes the puck finds a way into the back of the net vs. Philly," he said. "I'll take it."
The Flyers had chances to win in regulation and overtime. Giroux got a breakaway with 3:06 left in the third period but Howard got his left pad out to stop him on the post. With 1:07 remaining in overtime Giroux was stopped on another breakaway.
"[Giroux] is a top talent in the League and he's got shifty hands," Howard said. "Just hard work paying off in practice, doing a lot of breakaways, especially with [Dylan Larkin], and it's paid off."
Despite the missed opportunities Giroux felt the Flyers played well.
"We had our chances," he said. "We had a couple breakaways. [Howard] was pretty sharp on their side. … We had our chances to win, and even in overtime we had a couple chances, so I think we did a lot of good things to put ourselves in a position to win."
The Flyers took a 1-0 lead when Giroux one-timed a cross-zone pass by Voracek for a power-play goal at 6:28 of the first period, but Tatar's goal at 8:42 tied the game. Henrik Zetterberg bumped Manning off the puck just to the right of the Flyers goal, and Gustav Nyquist tipped it away from Mason. Zetterberg got it behind the Flyers net and sent it out front to Tatar, who scored for the first time in nine games.
"Defensively and taking care of the puck we weren't at our best the entire 65 minutes," Flyers coach Dave Hakstol said.
