New York, which won a 13-round shootout in Philadelphia on Saturday, lost for the first time (2-1).
Antero Niittymaki bounced back from the weekend loss and made 25 saves for the Flyers (1-1-1). Marcel Hossa won Saturday's shootout with the only goal in the lengthy tiebreaker.
In the rematch, Simon Gagne tipped Forsberg's right-circle feed under Henrik Lundqvist's pads on a 5-on-3 power play for his third goal of the season at 12:25 of the second period that made it 4-1.
New Rangers forward Brendan Shanahan scored his third of the season - all in New York's two home games - with 29 seconds left in the middle period. He fired in a hard slap shot off a nice feed from Michael Nylander during a power play to close the gap to 4-2.
It was the first power-play goal of the season for the Rangers.
Philadelphia scored twice within 59 seconds of the second period to take a 3-1 lead. Mike Knuble scored his first at 6:59, skating out unchecked from the right corner and deking Lundqvist on a backhander from close range. Geoff Sanderson followed at 7:58, scoring on a 2-on-1 break for his second of the season.
The Flyers came out aggressively at the start, swarming on the forecheck and forcing Lundqvist to make several difficult saves. Forsberg skated out of the right corner along the goal line and scored his second goal on a high, sharp-angle wrist shot from close in at 3:15 to give Philadelphia a 1-0 lead.
Rangers defenceman Thomas Pock scored his first at 16:33 to make it 1-1. Petr Prucha started the play by blocking a point shot in the New York zone and sending a nifty backhand pass off the sideboard as he fell to the ice to create a 2-on-1 break.
Shanahan skated down the left wing and sent a cross ice pass to Pock, who waited until Niittymaki went down and wristed the puck into the top of the net.
Notes: David Wright, Tom Glavine, Paul LoDuca and Chris Woodward of the New York Mets were in attendance and received an ovation from the crowd. They open the National League championship series at home against St. Louis on Wednesday night. ... The Rangers were 0-for-12 on the power play for the season and 0-for-3 in 5-on-3 advantages before Shanahan's goal. ... Shanahan tied Jari Kurri for 14th on the NHL career goal list with 601. ... Jaromir Jagr, who assisted on Shanahan's tally, has 33 goals and 60 assists in 71 games against the Flyers. ... Forsberg has five goals and 26 assists in 22 career games versus the Rangers