Valtteri Filppula scored twice in the final 3 minutes of regulation, including the tying goal with 3.8 seconds left, and then converted in the shootout to rally the Lightning past the skidding Islanders 3-2.
''When you're coming back from two down and get that first one, you get immediate confidence,'' said Filppula, a key free-agent signing by Tampa Bay last summer. ''That's a good sign when you get a great bounce late and win a game when you didn't play your best all night.''
Nikita Kucherov also connected in the shootout as the Lightning handed New York its 13th loss in 14 games (1-9-4). The only Islanders victory during that stretch came in a shootout last Tuesday at San Jose.
''It's unbelievable, it's frustrating, it's disappointing,'' said Islanders captain John Tavares, who angrily slammed his stick against the boards as he left the ice. ''We're not happy with the result.''
Filppula scored his second third-period goal off a scramble with 3.8 seconds left to force overtime. He also scored at 17:07 to cut New York's lead to 2-1. He has 12 goals on the season.
Nielsen also scored in the shootout, but the game ended when Tavares couldn't convert the final chance for New York against Ben Bishop.
''I think you earn what you get,'' Tavares said. ''We left two guys open right in the slot, and they're going to capitalize when they get their chances.''
Okposo scored his 11th of the season, driving the puck from the left point through traffic and past Bishop 11 seconds into the second. Tavares and Brock Nelson assisted as Radko Gudas was serving an interference penalty that carried over from the first period.
Nielsen made it 2-0 at 10:21 of the third, converting on a 2-on-1 break with Michael Grabner to beat Bishop to the stick side. It was the 11th goal of the season for Nielsen, who hadn't scored since Nov. 19.
Filppula ruined Evgeni Nabokov's shutout bid late in the third and eventually spoiled the entire night for New York.
The Islanders (9-19-7) lost their sixth straight home game - the past four in overtime or a shootout - and dropped to 0-16-5 when scoring fewer than three goals. They haven't won at home since Nov. 16, when they defeated Detroit 5-4 in a shootout.
Only Buffalo, with eight wins, has fewer than the Islanders.
''We just don't know how to win right now,'' Nabokov said.
Tampa Bay (20-11-3) snapped a seven-game road losing streak Sunday against Detroit and pulled out another one away from home.
The Lightning have been a surprise in the Atlantic Division with an especially young roster this season. They have 13 players who have played fewer than 100 NHL games. But they are anchored by 38-year-old center Martin St. Louis, who leads the team with 13 goals and 18 assists. He played his 1,000th NHL game earlier this season.
The teams meet at Tampa Bay on Jan. 16 and March 27.
The Islanders next take on the rival Rangers at Madison Square Garden on Friday.
''It's important how we respond in our next game after a tough loss like this,'' Islanders coach Jack Capuano said.
The Islanders were without defenseman Lubomir Visnovsky (concussion) for the 27th straight game. New York also was missing forward Casey Cizikas (jaw). ... Matt Carkner and Colin McDonald were healthy scratches for the Islanders. ... The Lightning were without defensemen Victor Hedman (lower body) and Keith Aulie (hand).