Gustavsson made 25 saves as the Leafs registered just their second win in six contests.
Michael Lombardi netted a pair of goals and Phil Kessel added a marker in Toronto's victory.
Evgeni Nabokov absorbed the defeat for the Islanders, yielding three goals on 35 shots.
New York had a three-game winning streak snapped.
Swim Week Miami Beach 2014 [PHOTOS]