Ryan Callahan's second career hat trick 2 victory.
Marian Gaborik added a goal and three assists for the Rangers, who have won all five of their meetings with the Flyers this season and increased their winning streak in the series to seven games.
Sergei Bobrovsky turned aside 21-of-26 shots in defeat.
The story of the game was the power play. New York was 3-for-7 with the man advantage, while Philly went 0-for-4.
The Rangers started the game with a power-play goal from Callahan at the 8:25 mark of the first period. After taking a pass from Gaborik, Callahan managed to score from a tough angle along the goal line.
Simmonds made it a tie game at the 13:03 mark. Andrej Meszaros' blast from the right point deflected off Simmonds' leg and past Lundqvist.
New York, though, scored again on the man advantage with 3:20 left to make it 2-1. Brad Richards controlled the puck at the top of the right circle and passed in front to Gaborik, who quickly redirected the puck past Bobrovsky.
The back-and-forth battle continued 6:36 into the middle stanza. A nice pass from Simmonds put Giroux on a breakaway. Lundqvist put his arm down along the line to stop Giroux's initial shot, but the Flyers forward was able to jam the puck into the net.
But the Rangers swung the momentum back in their favor with another power-play goal. The visitors got set up in the offensive zone, which resulted in Michael Del Zotto controlling the puck in front of the net. His pass across the crease led to Callahan's second goal of the contest.
New York put the game away with a pair of goals in the third stanza. Just 6:28 into the frame, Gaborik slid a pass from below the goal line to the right circle for Derek Stepan, who slid the disc to the slot. From there, Anisimov put the puck into the back of the net for a 4-2 margin.
Callahan completed his hat trick at the 11:25 mark. With Bobrovsky sprawled out on the ice, Callahan lifted the puck over the goaltender and into the net.
Both of Callahan's hat tricks have come against the Flyers...New York was without forward Ruslan Fedotenko after he took a shoulder to the head from Tampa Bay's Dominic Moore on Thursday...The Rangers have outscored the Flyers 29-10 over the past seven encounters, shutting them out twice...The Rangers scored three power-play goals in a game for the first time since March 15, 2011.