Zherdev got the first goal of the game midway through the second period when Mike Richards hit him with a long pass as he was stepping out of the penalty box. Zherdev skated in alone, deked a forehand and then delivered a backhand shot past Henrik Lundqvist.
The Flyers' right wing also scored with five minutes remaining to ice the victory, which allowed Philadelphia (21-7-5) to retain the NHL's best record.
Andreas Nodl and Ville Leino also scored and Boucher turned aside 24-of-25 shots for the victors.
Derek Stepan scored a third-period goal and Lundqvist ended the day making 35-of-39 saves in the Rangers' setback.