Nabokov made an in-close save on Victor Hedman in the second period, and Tavares had a power-play goal midway through the frame to help the Islanders improve to 4-1-2 over their past seven games.
"They're going to get chances, but the key is always what kind of chances they're going to get, and where are they going to get them, and how much time are they going to get," Nabokov said. "I thought we did a very good job on the big guys. This was a team effort in the zone."
Brad Boyes added an empty-net goal in the final minute of play.
Anders Lindback stopped 27 shots for Tampa Bay, which has lost eight of 10.
"It's just a weird thing," Lightning coach Guy Boucher said. "We're scoring tons of goals and we're not defending well. All of a sudden now we're defending well and we're not scoring goals. It's flip-flop, flip-flop. It's hard to take. The story of our year, we can't get everything together on the same day."
Lightning captain Vincent Lecavalier didn't play and is out indefinitely because of an undisclosed lower-body injury. Lecavalier, who was hurt Tuesday night against Florida, was placed on the injured list before Thursday's game.
New York was without speedy forward Michael Grabner, who was put on the injured list Wednesday because of a shoulder injury sustained Sunday in a game at Pittsburgh.
Tavares put the Islanders up 1-0 when he put an in-close backhander past Lindback during a power play at 10:22 of the second. Matt Moulson set up the goal with a backhanded pass from the low slot to Tavares, who was positioned near the post.
"He had his back to me and made a great pass and drew a couple of guys," Tavares said. "He probably could have put it in himself, but really made it easy. I just had a tap-in."
New York, which entered with the NHL's best road power play, had just the one advantage in the game. Tampa Bay failed to convert on its two chances.
"Especially this time of the year, the special teams are going to play a big part," Lightning left wing Ryan Malone said. "Their team got the goal and our team didn't."
Islanders left wing David Ullstrom left in the third period because of a lower-body injury.
Former Tampa Bay forward John Cullen, who won the Masterton Trophy in 1999 after returning to play after being diagnosed with cancer, dropped the ceremonial first puck. ... Tavares has scored eight power-play goals. ... Tampa Bay C Steven Stamkos had his three-game goal streak end. ... Islanders D Colin McDonald (illness) didn't play. ... The Lightning recalled forward Tyler Johnson from Syracuse of the AHL to take Lecavalier's roster spot. Johnson made his NHL debut.
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TAMPA, FL - MARCH 14: Steven Stamkos #91 of the Tampa Bay Lightning warms up prior to the game against the New...