After Steve Staios was benched two minutes for hooking Ted Purcell, Lightning forward Ryan Malone flicked one in on the power play to go up one-zip in the first.
Vincent Lecavalier joined the party in the second stanza to make it a two point lead before Steven Stamkos put Tampa Bay up 3-1 in the third period.
Brett Clark made it 4-1 with a tip-in shortly thereafter.
It was a disappointing loss for the Islanders, who drop to 3-2-0 with the loss while Tampa Bay starts to dig themselves out of the hole by improving to 2-3-2.