Mike Comrie and Doug Weight also scored for the Islanders. New York was coming off a 7-1 loss Monday to the Buffalo Sabres.
Vincent Lecavalier, Vinny Prospal and Ryan Malone had the Tampa Bay goals.
New Tampa Bay coach Barry Melrose is still seeking his first victory with the team. The Lightning have dropped four in a row - including two overtime defeats - to start the season.
Comrie put the Islanders ahead 1-0 on a rebound goal at 2:47 of the first. Weight made it 2-0 during a power play with 6:06 left in the second.
Lecavalier cut the Tampa Bay deficit to 2-1 at 3:43 of the third when he skated in from the right wing and scored from the low slot. Prospal tied it at 2 on an in-close rebound at 12:02.
Hunter extended his goal-scoring streak to three games in giving New York a 3-2 advantage with 6:09 left in the third. Malone pulled the Lightning even again at 3-all at 14:57 of the period.
Notes: New York G Rick DiPietro (undisclosed injury) hasn't play in any of the Islanders' four games this season. He was the backup Thursday. ... Tampa Bay D Paul Ranger (shoulder surgery) played for the first time this season. ... It was the 2,800th regular season game for the Islanders. ... Free agent D Marek Malik is working out with Tampa Bay and could soon be signed by the team.
