Colton Sissons also scored, and Anthony Stolarz made 26 saves for the Maple Leafs (1-1-0), who lost their season opener 3-2 to the Montreal Canadiens on Tuesday.
Toronto went 1-for-4 on the power play and 4-for-4 on the penalty kill.
Ilya Sorokin made 24 saves, and Emil Heineman scored a short-handed goal for the Islanders (0-1-0).
Sissons put the Maple Leafs up 1-0 at 7:14 of the first period. Cowan carried the puck out of the corner and fed Nick Paul, whose shot from the slot was redirected by Sissons at the top of the crease.
The Maple Leafs extended their lead to 2-0 while on a power play at 11:55. Morgan Rielly knocked down a waist-high clearing attempt at the blue line before finding Jack Roslovic at the left face-off dot. Roslovic's shot then produced a rebound off Sorokin's left pad, which Cowan jammed in near the right post.
Stolarz kept it a two-goal game at 6:42 of the third period when he reached back with his right pad to stop Anthony Duclair’s shot from the side of the net.
Heineman did cut it to 2-1 with his short-handed goal at 14:09. He beat William Nylander down the ice, received a saucer pass from Bo Horvat, and chipped the puck past Stolarz.
