The Islanders took advantage of their first power play to take a 1-0 lead 4:20 into the game. After Tampa Bay's Mike Blunden was called for roughing Ryan Strome, Okposo found a dead spot in the defense inside the left circle, took a passout by Nikolay Kulemin and beat Bishop to the top far corner for his second goal of the playoffs.
New York had two more excellent chances before the first period was 10 minutes old. At 9:11, Strome's tip-in try hit Bishop and slid under him, but a video review upheld the call on the ice that the puck did not cross the goal line. Less than 40 seconds later, Shane Prince picked up a rebound in the slot and hit the crossbar.
The Islanders also failed to capitalize later in the period when Lightning forward Ryan Callahan was assessed a double minor for roughing. But they ended the period up 1-0 after holding Tampa Bay without a shot for the final 12:05.
"You know there's going to be a push on the road," Bishop said of New York's first-period dominance. "They're feeding off this crowd. You try to keep them in there, just worry about the next save. You keep the team in and eventually they came through."
The Lightning picked up their game in the second period, outshooting the Islanders 11-6, but they were unable to score on three power plays, managing four shots on goal.
The Islanders will head for Tampa knowing that anything less than a win means their season is over.
"Probably our two best games of the playoffs, to be honest," forward Matt Martin said of New York's performance in Games 3 and 4. "We were getting the bounces in the Florida series. Maybe they're getting a little more of the bounces right now. We've just got to fight through it."