Andreas Nodl and Ville Leino also scored for the Flyers (21-13-1), who have won five straight and seven of eight. They have 49 points, best in the NHL.
Boucher has gone 6-0-1 in his last seven starts, including four of the previous five games, as the Flyers ended New York's three-game winning streak. The 33-year-old goaltender was in goal when the Flyers eliminated the Rangers on the final day of last season.
The Flyers also beat New York on Nov. 4 by the same score.
Zherdev scored Philadelphia's first goal just after serving a two-minute penalty for cross checking, when center Mike Richards fed him a cross-ice pass as he returned from the box. Alone, the former Ranger beat Henrik Lundqvist with a forehand-to-backhand shot to the glove side.
Zherdev scored his second goal on a power play, giving him 13 this season, including goals in three straight games.
Nodl made it 2-0 at 3:13 of the third, deflecting Claude Giroux's pass into the net.
New York's Dale Weise appeared to put the Rangers on the board, but his goal at 14:25 left in the game was disallowed when it was rule the he kicked it in the net.
Rookie Derek Stephan finally beat Boucher with a one-timer amid a flurry of Rangers shots for his ninth goal of the season. Alex Frolov fed him from behind the net with 11:37 left in the game, pulling the Rangers (20-14-1) within a goal.
Philadelphia quickly regained their two-goal advantage 1:40 later when Ville Leino redirected Kimmo Timonen's shot from just above the face-off circle, his eighth of the year.
Notes: Rangers LW Derek Boogaard missed the game with a shoulder injury. ... Ryan Callahan is expected to miss 6 to 8 weeks with a non-displaced fracture in his left hand, sustained blocking a shot Dec. 15 game against the Penguins. ... Flyers D Chris Pronger had foot surgery Friday and is out 4-6 weeks. ... The Rangers are 14-5-2 in their last 21 games in Philadelphia.