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). 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.
Lundqvist lost his shutout bid when Mark Streit scored a power-play goal 6:49 into the third.
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 goals. The first came at 2:14 when Carcillo forced a turnover by Mark 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 was celebrating 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 hard shot from the right circle.
New York had a two-goal lead despite recording only four shots.
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.
New York began that frame on a two-man advantage - the final 15 seconds of Hartnell's penalty and a full two minutes for Chris VandeVelde, who was called for goalie interference as the first period ended.
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.
NOTES: Philadelphia had a 17-13 shots edge in the first period despite being outscored 3-0. The Rangers outshot the Flyers 15-6 in the second. ... Emery stopped all seven shots he faced Saturday. ... The Rangers are 19-2-1 when they score first. ... Lundqvist has allowed fewer than three goals in four of his last six starts.