Nikita Kucherov scored for the Lightning (45-28-6), who lost forwards Tanner Jeannot and Pat Maroon in the second period to undisclosed injuries. Brian Elliott made 36 saves.
Tampa Bay, which lost 6-3 at the New York Rangers on Wednesday, will finish third in the Atlantic Division. The Toronto Maple Leafs secured second place with their 2-1 overtime loss at the Boston Bruins on Thursday.
"This is the NHL," Lightning coach Jon Cooper said. "To win in this league, you have to do the right things and play the right way and, if you don't, you risk being embarrassed and we've been embarrassed two nights in a row."
Steven Stamkos played his 1,000th NHL game for Tampa Bay. He had one shot on goal in 18:23 of ice time.
"[We're] playing teams that are fighting for their lives, and we're just not matching their desperation and execution," said Stamkos, the Lightning captain. "The last two games aren't the way we want to go."
Adam Pelech gave New York a 1-0 lead with a wrist shot through traffic at 3:46 of the second period.
Nelson made it 2-0 at 9:54 when he one-timed Samuel Bolduc's feed from behind the net, and Kyle Palmieri gave the Islanders a 3-0 lead 49 seconds later at 10:43. He took a pass from Nelson and scored with a wrist shot from the right circle.
Kucherov cut it to 3-1 at 16:47 with a wrist shot from the left circle after a feed from Brayden Point.
Pulock restored the three-goal lead with 20 seconds left in the second, scoring on a wrist shot after a feed from Nelson to make it 4-1.
"It was a pretty important goal," Pulock said. "Giving [up Kucherov's goal] late [in the second] got them back in the game, [but to be] able to get that one late in the period just kind of gives you a better feeling coming in for intermission."
