Mike Knuble also scored and Martin Biron made 34 saves for the Flyers, who have rebounded from a 0-3-2 start.
Bill Guerin and Andy Hilbert scored for the Islanders, who have dropped five straight games and six of their past seven.
The Islanders tied the game at 2-2 on a fluke goal at 12:40 of the third period. Hilbert's shot from in close bounced off the elbow of Flyers defenseman Ossi Vaananen and rolled behind Biron.
Carter broke a 1-1 tie at 15:29 of the period when he redirected Vaananen's long slap shot with a nifty backhand. Carter has scored points in six straight games (six goals, three assists).
New York's Joey MacDonald, who replaced Rick DiPietro in the net for the second straight game, stopped 25 shots. DiPietro is day to day with a lower-body injury.
Knuble put the Flyers ahead with a one-timer from the slot at 7:45 of the first period.
Guerin tied it on a power play 2:32 later with another one-timer from just inside the blue line.
Notes: The Flyers saluted the Phillies' World Series win with a 60-second video tribute on the ArenaVision screen midway through the first period. ... Knuble extended his point-scoring streak to four games (4-1-5 ). ... Islanders D Mark Streit (3-3-6 ) and C Doug Weight (0-4-4) each extended their point-scoring streaks to four games. ... The Flyers failed to score in the second period for the first time this season. ... The game was delayed for 5 minutes with 14.1 seconds left in the third period when a shot by Flyers D Braydon Coburn shattered a pane of glass along the side boards.