Jakub Voracek tallied the game-winner midway through the third period and Jason Akeson added his first NHL goal for the Flyers, who concluded the season with a fourth straight win.
Claude Giroux handed out his 200th career assist as Philadelphia finished with a 23-22-3 mark.
Kyle Turris got the only goal for the playoff-bound Senators, who wrap up their season with a rescheduled game Sunday at Boston.
Craig Anderson made 23 saves.
Celebrity Couples of 2014 [PHOTOS]