Matthew Lombardi scored twice and Phil Kessel once for the Maple Leafs, who won for the second time in their last six games.
Evgeni Nabokov allowed three goals on 35 shots for the Islanders, who had won three in a row.
These clubs face each other in Uniondale on Tuesday in their final game before the All-Star break.
Toronto scored within the first two minutes, as Nabokov let a Lombardi chance from the right side slide between his pads.
Gustavsson needed to make just five saves in the first and six in the second to make the one-goal edge stand up.
After minutes' worth of increased pressure in the New York zone, Kessel tapped in a Joffrey Lupul rebound at the left post at 8:10 of the third period for a 2-0 game.
Lombardi connected on a low wrister from the right circle with 3:39 to play.
Gustavsson posted his fourth career whitewash...Ed Belfour was the last Leafs goaltender to blank the Isles, a 2-0 victory in Toronto on January 20, 2004...Toronto-area native and Islanders forward John Tavares saw his 12-game point streak come to an end.