The Islanders remained in eighth place in the Eastern Conference, tied in points with the seventh-place New York Rangers, who hold the tiebreaker. Both teams lead the ninth-place Winnipeg Jets, who are below the postseason cutoff, by two points.
The Islanders (19-16-4) are trying to make the postseason for the first time since 2007. They have nine games remaining, while Winnipeg has eight, and the Devils 10.
"We're working toward what we are trying to accomplish, and we still have a ways to go," said Islanders leading scorer John Tavares, who assisted on Josh Bailey's first goal midway through the first period. "We still have much we can do better. But we are excited to be in this position."
Michael Grabner also scored, and Andrew MacDonald added an empty-net goal at 19:46 to make it 4-2 for New York, which won for the sixth time in eight games.
The Islanders have five straight home wins against Tampa Bay and are 10-2 in their last 12 at Nassau Coliseum versus the Lightning.
"We battled hard and we continue to do little things well which bring big results," Islanders coach Jack Capuano said. "Our leadership is strong, and we are showing it."
Martin netted the go-ahead goal when his soft wrist shot from between the circles fooled goalie Ben Bishop, who appeared to be screened. Martin has three goals this season.
The Islanders have won three straight at home overall for the first time since December 2011-January 2012. They host the Philadelphia Flyers on Tuesday, and the Rangers on April 13.
"We're playing big games and we're playing well," said Islanders right wing Kyle Okposo, who assisted on Bailey's goal. "We have to keep it going."
Grabner, who took the place of ill left wing Matt Moulson on the top line with Tavares and Brad Boyes, opened the scoring 14:45 in with his 12th goal.
Grabner intercepted a clearing attempt by defenseman Sami Salo and fired the puck past Bishop, who was making his second start for Tampa Bay after he was acquired from Ottawa on Wednesday. Tavares, who leads the Islanders with 23 goals and 40 points, assisted on the goal.
"This is big for the guys in the room because they are seeing results," Tavares said. "The steps we've been taking are paying off."
Panik made it 1-1 at 4:44 of the second with a snap shot from the left circle for his second goal of the season.
Bailey put the Islanders back on top at 8:22 of the second when he jammed his seventh goal of the season past Bishop off a scramble in front.
"We know that with nine games left we still have plenty of work to do," Bailey said. "We have to play our best."
Carle, who also had an assist, tied it again at 4:00 of the third period when he scored off a rebound of Steven Stamkos' shot.
The Islanders have been tied or ahead in the third period in 33 of 39 games. They are 18-2-2 when scoring at least three goals and 1-14-2 fewer than three.
"We did a good job defensively," Capuano said. "We stayed with our structure."
The Lightning were missing defenseman Victor Hedman. who sustained a lower body injury against Carolina on Wednesday. Defenseman Matt Taormina was recalled from AHL Syracuse to take Hedman's place.
"We didn't do a good job of puck management," said Lightning coach Jon Cooper, who replaced Guy Boucher on March 25. "We have to do a better job of that if we want to be successful."
The Islanders play three of their next four at home before ending the regular season with five road games. The Islanders started 2-8-1 at home but are 6-3-1 there since March 1. The Islanders are 11-5-2 on the road.
The Islanders swept the three-game season series from the Lightning.
Moulson's consecutive games streak ended at 284. He hadn't missed a game in his Islanders career. The only Islanders with longer streaks are Billy Harris (576) and Bob Nystrom (301). ... Islanders LW Jesse Joensuu made his season debut. ... The Lightning were without C Dana Tyrell. ... Nabokov has started all but six of the Islanders' 39 games.
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UNIONDALE, NY - APRIL 06: Michael Grabner #40 (C) of the New York Islanders scores at 14:45 of the first period...