Danny Briere tied the game late in regulation 3, at Nassau Coliseum.
Scott Hartnell, who had just exited the box after a hooking minor, then carried up the ice and dished to Briere, who shifted between the circles and scored on a high wrister.
Andrej Meszaros and Hartnell also tallied for the Flyers, who snapped a two- game slide.
Bobrovsky picked up the win by halting 23 shots. Ilya Bryzgalov got the start but was pulled after allowing three scores on nine shots in the opening 20 minutes.
Rick DiPietro surrendered four goals on 33 shots.