TAMPA, Fla. -- Shane Prince scored twice in the final three minutes of the first period, and the New York Islanders held on for a 5-3 road win over the Tampa Bay Lightning, opening their second-round series Wednesday night at Amalie Arena.

New York led 4-1 in the third, but the Lightning got goals from Nikita Kucherov and Valtteri Filppula to pull within a goal with 2:32 left in a furious comeback. After Tampa Bay pulled its goalie in the final two minutes, New York got an empty-net goal from Cal Clutterbuck to seal the win.

Prince scored both goals from just in front of the Lightning goal, getting passes from Ryan Strome and getting the puck past Lightning goalie Ben Bishop, who left after a fourth goal midway through the second period.

The Islanders came in with much less rest after eliminating the Florida Panthers with back-to-back double-overtime wins, but they now have a 1-0 series lead as the series continues in Tampa on Saturday afternoon.

Tampa Bay got a goal in the third period from Kucherov -- his team-best sixth of the playoffs -- to cut the lead to 4-2 with 12:19, but New York had the game in hand at that point. New York goalie Thomas Greiss gave up a goal just three minutes into the game, but shut out the Lightning for the next 45 minutes, facing a slew of shots in the third period and finishing with 33 saves. Filppula's goal made it a one-score game with 2:32 left, but Greiss held on in the final two minutes.

Bishop, who hadn't allowed more than two goals in any of five first-round games against Detroit, gave way to backup Andrei Vasilevskiy.

After briefly trailing 1-0, the Islanders set the tone for the series with three goals in the first period, then chased Bishop with a fourth goal midway through the second period.

Tampa Bay had jumped out early, with Ondrej Palat scoring his second goal of the postseason on a spin pass from Jonathan Drouin for a 1-0 lead just 3:05 into the game.

Shortly after, the Islanders' Casey Cizikas sent Lightning forward Erik Condra flying into the boards with a hit that left him motionless on his back on the ice for a minute before he was helped off by trainers.

Not even three minutes after the Lightning goal, the Islanders answered, with Travis Hamonic firing a long shot that went through Bishop's legs to tie the score at one with 14:16 left in the first period.

Tampa Bay killed off two New York power plays in a span of five minutes, but Prince scored twice in the final 2:32 of the period for a 3-1 lead.

Prince was open on the far side of the net on a pass Strome for the go-ahead goal, and then with just 2.1 seconds left in the period, Strome was behind the net and found Prince in the same spot to beat Bishop for a 3-1 lead.

Tampa Bay outshot New York early in the second period, but a hooking penalty on Jonathan Marchessault -- who had been a healthy scratch in all five games against Detroit -- gave the Islanders a power play. With 11:01 left in the period, John Tavares went top shelf to beat Bishop for a 4-1 lead for his sixth goal of the playoffs.

Islanders coach Jack Capuano missed part of the third period after he was hit in the face with a puck.

Capuano was back on the bench with a cut on his nose for the final two minutes of the game, after a pass from Lightning center Alex Killorn went into the Islanders bench, catching the coach in the face.

He was helped off the bench with a towel covering his face, but returned for the end of the game. Assistant Doug Weight stepped in while he was sidelined.

NOTES: The Islanders played without C Josh Bailey, who didn't make the trip because of an upper-body injury. He played in all six games in the opening round of the playoffs but was a team-low minus-4 in the series. ... RW Steve Bernier, who dressed in only two games against Florida and had no points, dressed in Bailey's place. ... The Lightning fielded the same lineup they did throughout the five-game series with Detroit -- they are still waiting to get D Anton Stralman, RW J.T. Brown and C Steven Stamkos back from recent injuries. Stamkos has returned to practice in a non-contact jersey but is likely still the farthest from a return.