James van Riemsdyk scored Philadelphia's first goal, firing a behind-the-net pass from Mike Richards past Islanders goalie Dwayne Roloson.
Less than two minutes later, Carter powered a pass from Marc-Andre Bourdon behind Roloson.
With 52 seconds left in the first period, a shot to Roloson's left by Scott Hartnell deflected to Carter, and the center flipped in a backhand.
Sergei Bobrovsky made 32 saves for Philadelphia. He lost his shutout 6:29 in the final period when Krys Kolanas beat him amid a scramble in front of the net on a power play. The rookie is competing with Johan Backlund to be Brian Boucher's backup while Michael Leighton misses the first month with a back injury. Roloson stopped 32 shots.
Philadelphia's Ville Leino (hip) and Blair Betts (right shoulder/left knee) played in their first game since having offseason surgeries.