The Islanders ended a two-game skid and won for just the 15th time in 46 games this season.
New York scored the first four goals of the contest, Grabner getting things going by tipping in a shot from Rob Schremp 7:26 into the game. Matt Moulson, P.A. Parenteau and Jack Hillen added goals to give the Islanders a 4-0 lead with 5:27 to go in the third period.
Nathan Gerbe then tallied twice in a span of 5 seconds late in the third and Grabner added an empty-net goal with 2 seconds to play.
Nathan Lawson opened in goal for the Islanders but suffered an injury to his left knee in the first period and was replaced by Kevin Poulin. Poulin allowed two goals on 28 shots the rest of the way.
Buffalo also changed goaltenders during the game, with Ryan Miller being removed midway through the first period after giving up two goals on 10 shots. Patrick Lalime finished the game by saving 16-of-18 shots.