Mike Richards and Chris Pronger added power-play goals for Philadelphia which extended its season-best winning streak to five games.
Despite the loss, the Rangers are 14-4-2 in their last 20 games in Philadelphia.
The last time these teams met was an eventful 3-2 shootout win by the Flyers in Philadelphia that them into the playoffs as the seventh seed. They went on to represent the Eastern Conference in the Stanley Cup finals against the Chicago Blackhawks.
In the second period, Brandon Dubinsky fired a rebound from Michael Del Zotto's shot past goalie Sergei Bobrovsky. Dubinsky leads the Rangers with eight goals in 12 games.
Philadelphia scored the next three goals against Henrik Lundqvist, who started Thursday despite being hit on the right side of his neck in practice Wednesday.
Richards tied the game at 5:12 with a one-timer from one knee. More than four minutes later, Betts gave the Flyers the lead when he fetched his own rebound and backhanded a shot past Lundqvist. Zherdev added the last goal when the pass he sent toward the net took a funny hop and bounced over Lundqvist's shoulder.
Notes: Flyers C Danny Briere served the second game of his three-game suspension. He'll also miss Saturday's game at the New York Islanders, returning Sunday at Washington. ... Rangers RW Ryan Callahan had his seven-game point streak snapped. ... Flyers D Andrej Meszaros returned to the lineup after missing two games with a mild concussion. ... Former Flyers forward and current broadcaster Bill Clement was sworn in as an American citizen between the first and second periods. He recited the Pledge of Allegiance as part of the ceremony.