The Flyers have captured five in a row and six out of seven to take early command in the Atlantic Division.
Bobrovsky allowed a power-play goal to Brandon Dubinsky 1:53 into the second but the Flyers scored three times before the end of the period.
Mike Richards tied it on the power play, Blair Betts put Philadelphia in front with a backhander and Nikolay Zherdev put a wrist shot past Henrik Lundqvist with 4:40 to go in the second.
Chris Pronger added a power-play goal 3:07 into the third.
The Rangers had won their previous two games. Lundqvist gave up the four goals on just 21 shots.