Philadelphia won for the 26th time in 28 meetings with the Islanders since the beginning of the 2007-08 season. It was the Flyers' fourth straight victory overall.
New York lost for the fourth time in five outings following a three-game winning streak.
Kyle Okposo brought the Islanders within one just 22 seconds into the third and it remained a 2-1 game until Couturier all but clinched it with his eighth of the season.
John Tavares gave the Islanders brief hope by scoring with 16 seconds remaining in regulation.
Sergei Bobrovsky picked up the win by stopping 33-of-35 shots. Evgeni Nabokov saw his record slip to 6-11, giving up three goals on 22 shots.