Thomas Pock, Martin Straka and Petr Prucha, each had a goal and an assist, and Ryan Callahan also scored for the Rangers, who won for the sixth time in seven games and held onto seventh place in the Eastern Conference.
New York is one point up on Montreal and two ahead of Toronto in the race for the seventh and eighth spots in the Eastern Conference. Both Montreal and Toronto won their respective games Saturday night.
Ben Eager had two goals, and Braydon Coburn and Ryan Potulny added one each for the Flyers, who have dropped two straight and six of seven. Nathan Guenin had two assists for his first NHL points.
Biron, 5-7-1 since being acquired from Buffalo on Feb. 27, was replaced by Antero Niittymaki at 7:15 of the second period after he allowed goals to Jagr and Straka within a minute to give the Rangers a 5-2 lead.
Biron saved only 17 of 22 shots. Henrik Lundqvist had 33 saves for the Rangers.
Jagr scored his second of the game when he snapped a wrist shot over Biron's blocker. Straka scored from the left side after taking a cross-ice pass from defenceman Marek Malik.
After Coburn picked up a loose puck and scored on a one-timer, Prucha made it 6-3 on a power play with 50 seconds left in the second period. Potulny scored on a deflection at 1:59 of the third.
Pock and Jagr each had a goal and an assist in the first period as the Rangers took a 3-1 lead.
Pock put the Rangers ahead at 3:32 when he scored on a wrist shot from the top of the left circle.
Eager tied it 24 seconds later when he picked up a loose puck near the right boards, skated in and shovelled in his own rebound.
New York regained control at 5:52 when Callahan scored on a rebound.
The Rangers increased their lead to 3-1 at 11:59 when Jagr skated into the slot. He appeared to momentarily lose control of the puck, but reached out and slid it past Biron, who allowed the three goals on only eight shots.
Eager brought the Flyers to within 3-2 at 4:00 of the second period when his shot from the left side bounced off the stick of New York's Ryan Hollweg.
Notes: The Rangers won the season series 6-2. ... D Pock has six points (3 goals, 3 assists) in the last seven games. ... Biron denied LW Brad Isbister's short-handed breakaway attempt midway through the first period. ... Niittymaki played in his 100th NHL game. ... RW Jagr, C Straka, and LW Brendan Shanahan each have a team-high 28 goals for the Rangers.