Coach Jack Capuano returned to the Islanders and guided them to their first win of the season. He missed the opening-night loss to New Jersey on Saturday because of surgery to remove a kidney stone.
Michael Grabner, Matt Martin and Kyle Okposo scored in a 12-minute span of the second period to put the Islanders ahead 3-0. Ullstrom gave New York a four-goal lead 91 seconds into the final period.
Martin St. Louis, Benoit Pouliot and Steven Stamkos scored in a 5 1/2-minute stretch, pulling Tampa Bay within a goal with 12 minutes left. The Lightning couldn't get anything else past Evgeni Nabokov, who stopped 23 of 26 shots.
Anders Lindback allowed all four of New York's goals on 44 shots.
For the first 40 minutes, New York was much tighter defensively than it was in the 2-1 loss to the Devils. The Islanders took away the middle of the ice, forcing the potent Lightning to the perimeter.
The clogging of the defensive zone allowed the Islanders to force mistakes. New York took advantage of those turnovers with goals by Grabner, Martin and Okposo.
Grabner opened the scoring 5:38 into the second period with a power-play goal. His first goal of the season also marked New York's first lead of the season.
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Martin and Okposo scored consecutive goals in a 62-second span to make it 3-0. As Martin's penalty for holding expired, Tavares sprung him for a semi-breakaway and the New York forward snapped past Lindback's stickside at 16:23 to give the Islanders a 2-0 advantage.
Okposo then came down on a 2-on-1 and scored his first goal of the season.
Ullstrom's off-wing goal 1:31 into the third grew the lead to 4-0 before the Lightning rallied.
St. Louis' goal was his third in two games while Stamkos and Pouliot got their first. Stamkos scored 60 last season and has twice led the NHL in goals.
NOTES: New York went 1 for 7 on the power play. Tampa Bay was 0 for 3 on the man advantage. ... Vincent Lecavalier played his 1,000th NHL game. The No. 1 overall pick in the 1998 draft, Lecavalier has played his entire career with the Lightning. ... The Lightning made a minor trade Monday morning, acquiring forward Jean-Francois Jacques from the Florida Panthers for future considerations. Jacques, 27, has played in 166 NHL games with the Edmonton Oilers and Anaheim Ducks. He had seven points (five goals and two assists) in 24 games with the Panthers' AHL affiliate, the San Antonio Rampage.
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