Matt Pettinger had the only goal for the Lightning, losers of six straight (0-4-2).
Mike McKenna made 18 saves for Tampa Bay.
The Islanders scored 23 seconds after the opening faceoff. From the left side, Park spun around and sent a quick wrist shot past McKenna for his 14th goal of the season.
Tampa Bay came out firing pucks at Danis to start the second period, but he turned everything aside. Later in the period, the Islanders capitalized on a power play to take a 2-0 lead.
Off a faceoff, Martinek wound up with the puck at the right point. He moved to the top of the right circle and blasted a shot over McKenna's glove-side shoulder at 14:52.
Pettinger got the Lightning on the board with a power-play goal at 16:36.
The Islanders gave themselves a bit of breathing room with another power-play goal, this time with Bailey connecting off a beautiful feed from Blake Comeau at 9:14 of the final period.
Notes: The Islanders recalled five players from Bridgeport on an emergency basis: forwards Mitch Fritz, Mike Iggulden, Jesse Joensuu and Joel Rechlicz, and defenseman Jamie Fraser. Fraser made his NHL debut. ... Tampa Bay recalled defenseman Vladimir Mihalik from Norfolk.
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