Chris Kreider got his team-leading 12th goal in the second period to help the Rangers win their third straight and fourth in five (4-0-1). Lundqvist has allowed just eight goals in New York's past four games.
"I got tested early, and you gain confidence when you make a couple of good saves," said Lundqvist, who has given up fewer than three goals in four of his last six starts. "I'm happy with the way I am playing.
"It definitely helps when we play the way we play in front of me and make good decisions all over the ice."
New York, 8-2-1 in its last 11, is tied in points with Washington for second place in the Metropolitan Division -- one ahead of Philadelphia. The Rangers have won seven straight against the Flyers at home, outscoring them 28-8.
Ray Emery rebounded after the rough first period and finished with 31 saves for the Flyers, who lost 6-3 on Saturday to Tampa Bay -- ending a 10-game, home-winning streak. Philadelphia had won seven of eight before the weekend sweep.
"It's frustrating," Emery said. "I've got to make some saves, and we've got to come out better. Anytime you put yourself in a hole like that against a team that is playing well like they are, you don't give yourself much of a chance."
Lundqvist lost his shutout bid when Mark Streit scored a power-play goal 6:49 into the third. Rangers coach Alain Vigneault offered no theories about how Lundqvist has gotten back on his game after an up-and-down first half.
"To tell you the truth, I am just focused on one thing with him -- stopping the puck," he said. "How he does it, I don't really care that much."
The Flyers were hurt by being short-handed six times in the first two periods.
"A lot of guys kill a lot and get a little tired, and the other guys are sitting on the bench and just waiting to get back onto the ice," captain Claude Giroux said. "We need to find a way to stay out of the box."
The Rangers came out flying and grabbed a 2-0 lead just 2:42 in on goals 28 seconds apart by Carcillo and Nash.
Sloppy play by the Philadelphia defense contributed to both. The first came at 2:14 when Carcillo forced a turnover by Streit behind the net. Carcillo charged out in front and backhanded a shot past Emery for his second of the season and his first in three games with the Rangers since he was acquired from Los Angeles.
Before that goal was announced, New York celebrated again when Nash netted his 11th of the season and fourth in four games. Philadelphia defenseman Braydon Coburn lost the puck behind the net to Kreider, who quickly sent a pass out to the charging Nash for a shot from the right circle.
New York had a two-goal lead despite recording only four shots.
"They were way quicker than us in the first period, had the puck more than us in the first period, and we ended up getting down right away," Flyers coach Craig Berube said. "We've got to be more ready."
Philadelphia got its offense cranked up when Rangers defenseman Dan Girardi was sent off for interference at 6:20. The Flyers had six shots during the advantage but Lundqvist was sharp and turned them all aside.
Things didn't go nearly as well for Emery, who replaced an ineffective Steve Mason on Saturday after two periods. He gave up his third goal of the period at 9:24 when Brassard one-timed a shot from the left circle after Mats Zuccarello fed a pass to him from the left corner. Brassard, who has eight goals this season, has scored in consecutive games after going 10 without one.
The game turned a bit chippy late in the period, with Philadelphia's Scott Hartnell being called for roughing with 1:45 left. Carcillo, formerly of the Flyers, yapped at several players on the Philadelphia bench after he took the seat closest to the partition between the two sides.
Carcillo fought Luke Schenn off a faceoff before the midway point of the second period.
"I just got here, and from what I can see, when we do the little things right and play the game plan that we want to play against our opponents, we seem to have success," Carcillo said.
Emery was much sharper in the second, allowing only Kreider's power-play goal with 6:42 left and stopping 14 other drives. His best save came with 10:13 remaining when he denied Zuccarello on the doorstep.
Philadelphia had a 17-13 shots edge in the first period. ... Emery stopped all seven shots he faced Saturday. ... The Rangers are 19-2-1 when they score first. ... The Flyers had killed 26 consecutive penalties, dating to Dec. 28 at Edmonton, before Kreider's goal. ... Philadelphia C Vincent Lecavalier earned his 500th NHL assist.