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 last seven games.
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.
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.
New York entered with the NHL's best road power play.
NOTES: 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 eight