Karri Ramo started in net for the Lightning and stopped 13 shots before he was pulled for Mike McKenna, making his NHL debut.
McKenna made 11 saves.
Vincent Lecavalier scored for Tampa Bay, which has lost three consecutive games after winning three in a row.
Hunter's power-play goal made it 1-0 in the second and the Islanders extended the lead by scoring twice in a 93-second span.
At 8:29, Streit's right-point shot deflected off Ramo and in. Martinek then converted from the right point, chasing Ramo from the game.
Tampa Bay's best chance to score in the period came with just over two minutes left, when Vaclav Prospal hit the post on a wrist shot.
Tampa Bay finally broke through at 3:05 in the third. With 2 seconds left on a two-man advantage, Lecavalier's wrist shot from the top of the right circle got past Danis.
The scoreless opening period featured 11 shots for Tampa Bay, seven for New York, and a fight between star forward Lecavalier and Islanders enforcer Tim Jackman.
Notes: One of the bright spots on the Lightning, goaltender Mike Smith, was scratched. He's listed on the teams injury report as day to day with an upper-body injury. ... On the Islanders' side, Joey MacDonald, who missed time with a groin strain, was healthy enough to serve as Danis' backup.