New York fell behind 3-1 after one period, tied it in the second and then continued what turned out to be a streak of five unanswered goals to take charge in the third.
The Islanders have won two in a row after a season-opening loss. Toronto is 2-2 on the season.
Mark Streit and Brad Boyes scored the only goals of the second period to bring the Islanders back into a 3-3 tie and Grabner put New York in front for good 3:23 into the third.
Keith Aucoin and Matt Moulson added goals over the next 8 minutes to boost the Islanders' lead to 6-3. Grabner's second goal was scored into an empty net with 1:10 to play.
Evgeni Nabokov made 39 saves to get the victory. Ben Scrivens started in goal for the Maple Leafs, but was removed in the third period after giving up five goals on 25 shots.