Toronto's Matt Frattin was assessed a penalty for shooting the puck over the glass and Moulson capitalized with 6:04 remaining, collecting a loose puck at the side of the net and poking it past Maple Leafs goalie James Reimer.
PA Parenteau scored less than 2 minutes later and Moulson added an empty-netter for the Islanders, who won for second time in seven games.
Josh Bailey and David Ullstrom also scored and John Tavares added three assists for New York.
Evgeni Nabokov earned the victory with only 12 saves.
Notable deaths of 2014 [PHOTOS]