Anton Forsberg made 34 saves in the Senators (9-17-2) net while Tim Stützle, Alex Formenton and Artem Zub scored. Philadelphia (12-12-5) had goals from Claude Giroux, Oskar Lindholm, Joel Farabee and Travis Sanheim as Martin Jones stopped 28 shots.
"Of course we'd like to have an extra point but like every game, you can learn from a lot of different things so I think that's what we're going to do," Brady Tkachuk said.
After Ottawa had erased a 2-0 deficit in the second period, they had their first lead of the night with 6:17 to play as Zub's point shot evaded traffic to beat Jones for his second of the season.
It was a short-lived lead however as Farabee tied the game just 52 seconds later as his goalward shot took an unfortunate bounce off of Thomas Chabot and beat a moving Forsberg.
The Flyers won the game 1:35 into overtime as Chabot's clearing attempt hit a stanchion in the glass, fell onto the stick of Cam Atkinson who would feed Sanheim for the game-winner.
"It's a tough bounce," Smith said. "I don't know what else to say. They didn't create anything. They just threw it at the net."
In the opening frame, Farabee hit the crossbar inside 30 seconds on an odd-man rush but the Flyers did have the lead at 4:19 as from behind the net Lindblom fed Giroux out front in the slot for his 11th of the season.
The Flyers lead was doubled at 7:32 as Lindblom fired a shot goalwards from the top of the right circle that hit the stick of Thomas Chabot and redirected past Forsberg.
"We weren't ready to play when the game started," Smith said. "That's probably as bad of a 10-minute stretch we've had in a long time."
Ottawa came flying out of the gates in the second and managed to tie the game within the space of 1:13. Stützle scored his fifth of the year at 2:09 as he beat Jones from below the left faceoff circle on a rush down the left wing before Formenton's second short-handed goal of the season made it a 2-2 game at 3:22.
"I feel really confident right now," Stützle said. "But Formenton is playing really really well right now too and I love playing with him."
With his goal, Stützle tied the Sens' franchise record for most road goals by a teenager with 13 as he shares the record with Alexandre Daigle. Formenton's two short-handed goals this season puts him in a tie for first place in the NHL in that category.
The Sens' game against Boston scheduled for Sunday was postponed due to the Bruins' Covid-19 outbreak. The Senators are set to face St. Louis on Tuesday.
