Bill Guerin, signed as a free agent in the offseason, scored to give Islanders a 3-0 lead in the first period.
Sergei Kostitsyn scored the only goal for the Canadiens, who played in front of a partisan crowd of almost 7,000 fans at the Moncton Coliseum.
Sim's first goal came at 7:29 of the first period when he stuffed it past goalie Cristobal Huet. He made it 2-0 with 5:20 left in the first period when he deflected a centering pass from Marc-Andre Bergeron through Huet's pads.
Guerin, who has been made the Islanders' captain, scored 1:46.
Kostitsyn scored at 4:43 of the third period, putting a wrist shot past Wade Dubielewicz, who had replaced Rick DiPietro to start the third period.