The decision made a winner of Islanders Coach Jack Capuano, who missed Saturday's season-opening 2-1 loss to New Jersey due to a kidney stone attack. He was back behind the bench Monday.
Grabner's power-play goal 6:50 into to contest came off assists by Mark Streit and New York goaltender Evgeni Nabokov.
Matt Martin and Kyle Okposo scored in a 4-minute span later in the period and David Ullstrom made the score 4-0 91 seconds into the third period. All the goals were against Tampa Bay's Anders Lindback, who still made 40 saves.
Although Nabokov, who ended up with 23 saves, had a shutout to that point, he allowed three goals in about 5 1/2 minutes of the final period and Tampa Bay pulled within 4-3 with 12 minutes to go.