Jeff Halpern, Nick Tarnasky and Jason Ward had the other Lightning goals. Tampa Bay, last in the Eastern Conference, won for just the second time in 12 games.
Bill Guerin, Ruslan Fedotenko, Ben Walter and Mike Comrie scored for the Islanders, who have lost five of six. New York started play 12th in the Eastern Conference and seven points behind eighth-place Philadelphia, which played at Toronto.
New York goalie Rick DiPietro allowed eight goals on 44 shots.
Ouellet put the Lightning ahead 1-0 with a power-play goal at 6:51 of the first. Halpern stole the puck from DiPietro behind the net and passed it to Ouellet in the low right circle.
Lecavalier made it 2-0 during a 5-on-3 power play with 7:51 left in the first.
Guerin cut the Islanders' deficit to 2-1 at 17:05 of the first. New York tied it at 2 on Fedotenko's goal at 4:16 of the second.
Halpern put Tampa Bay up 3-2 nine minutes into the second. Mathieu Darche skated in from the left wing, drew DiPietro toward him, then skated behind the net and found Halpern all alone in the low right circle. The Lightning took a 4-2 advantage when Tarnasky scored his first goal in 16 games with 5:11 left in the second.
Lecavalier jammed a puck past DiPietro at 4:58 of the third to extend the Lightning lead to 5-2. After Walter scored a power-play goal with 9:58 left, Lecavalier completed his hat trick from the right circle at 17:43. Ouellet, at 18:15, and Ward 10 seconds later made it 8-3.
Comrie closed out the scoring with 36.4 seconds remaining.
