Kuba tapped in a perfect pass from Eric Perrin that left goalie Rick DiPietro in a defenceless position. DiPietro made his first start after missing most of three games because of injuries sustained in a mid-ice collision with Montreal's Steve Begin one week earlier.
The loss was the fourth straight on a road trip for the Islanders, who rallied from a 2-0 deficit with three second-period goals against Johan Holmqvist, an embattled goaltender who rebounded from the Lightning's 7-1 loss to Washington on Sunday to beat New York for the fourth time.
Tampa Bay swept the season series from the Islanders 4-0 and has beaten New York eight consecutive times.
Perrin scored a power-play goal in the opening period and Lecavalier's second-period goal made it 2-0. Richard Zednik, Richard Park and Miroslav Satan scored for New York before Tampa Bay's Jason Ward scored less than five minutes into the third period to make it 3-3.
Holmqvist stopped 21 shots for the Lightning. DiPietro finished with 36 saves.