The teams lingered on the ice for several minutes after the first-period horn, with the Rangers seemingly upset by a check from Brayden Schenn in front of New York's bench late in the period.
The Flyers scored twice in the opening period, with the goals coming 1:06 apart. Lecavalier opened the scoring at 7:04 on a goal that went off Rangers defenseman Anton Stralman.
"That's huge," Lecavalier said. "You want to get that first goal and we got that."
Brayden Schenn first was credited with the goal, but it was changed in between periods.
Couturier followed with his 10th goal of the season at 8:10, beautifully deking past Rangers goalie Henrik Lundqvist and roofing the puck with a forehand shot into an empty net from a difficult angle.
It looked as if the Rangers cut the deficit in half early in the second period, but Benoit Pouliot's apparent tally was waved off because Pouliot deflected the puck past Flyers goalie Steve Mason with a high stick. Mason finished with 33 saves.
Mason was pulled in Thursday's defeat to San Jose, and he was happy to bounce back with a victory. The fact that he outdueled one of the game's premier goalies was secondary.
"It feels good," Mason said. "But I wasn't going out there (thinking) Steve Mason versus Henrik Lundqvist. I was trying to help the Flyers beat the Rangers, and that's what we did."
New York got on the board a few minutes later when Kreider tipped Rick Nash's pass past Mason and just inside the post from close range.
After Kreider missed a great chance to tie the game when his backhanded attempt at an empty net went wide with 10 minutes left in the period, Brassard's power-play goal at 11:42 of the second tied the game at 2. Brassard's slap shot from the slot after a perfect pass from Brad Richards went off Mason's pads and through his legs.
Simmonds beat Lundqvist through the legs on a forehand shot from a tough angle on the power play at 13:23 to put Philadelphia back in front 3-2.
"I read a high shot and he went five-hole," Lundqvist said. "I thought I was patient on the shot; he just beat me. I thought overall we played a really good game and created a lot of good chances. Disappointing, obviously, but I thought we did a lot of good things."
Philadelphia had an apparent goal waved off 3½ minutes into the third period when the officials ruled that Lundqvist had covered the puck even though it trickled into the goal. Mason kept the Flyers in front with a strong, sprawling pad save on Stepan from just in front of the crease with 10 minutes left.
Luke Schenn provided an insurance goal with 3:45 left, beating Lundqvist with a wrister from the slot.
Lundqvist, who didn't start the Rangers' first game following the Olympic break after helping Sweden earn the silver medal in Sochi, finished with 27 saves. He entered the Olympic break having won his last five starts. In his last 14 games against Philadelphia entering Saturday, Lundqvist was 12-2-0 with a 1.77 GAA.
Philadelphia defenseman Kimmo Timonen returned to the lineup after sitting out Thursday's 7-3 loss to San Jose to rest after returning from Sochi and had two assists. Timonen helped Finland to the bronze medal.
Philadelphia won for the fourth time in the past 16 meetings with the Rangers.
Rangers RW Derek Dorsett returned to the lineup for the first time since breaking his fibula on Jan. 3. ... New York center Mats Zuccarello missed his second straight game after fracturing his left hand in the Olympics. ... Flyers backup goalie Ray Emery (lower-body injury) wasn't available. Cal Heeter, who never has played in an NHL game, was called up from the AHL's Adirondack Phantoms to back up Mason. Emery was injured in Thursday's loss to the Sharks after he replaced Mason in the second period. Berube said afterward that Emery wouldn't make the trip to Washington for Sunday's game, and the coach declined to name his starting goalie for the matchup.
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PHILADELPHIA, PA - MARCH 01: Cam Talbot #33 of the New York Rangers looks on during warmups prior to his game...