Filip Kuba notched the game-winner with just goal third period to 4, in the back end of a home-and-home set from Scotiabank Place.
Daniel Alfredsson, Chris Neil, Erik Karlsson and Nick Foligno totaled a goal and assist each for the Senators, who have won five of six and bounced back from an overtime loss in Philly on Saturday afternoon.
Craig Anderson stopped 33 shots for the victory.
Matt Read, Sean Couturier, Marc-Andre Bourdon and Andrej Meszaros scored for the Flyers, whose win streak was halted at two games.
Ilya Bryzgalov was tagged for five goals on 37 shots in defeat.