Brock Nelson extended the Islanders' lead to two midway through the third period, cleaning up his own rebound after a turnover behind the Lightning net.
Victor Hedman scored minutes later to get the Lightning back within a goal but video review revealed that Anthony Cirelli had entered the zone ahead of the puck and the goal was disallowed.
Nelson added his second goal of the game with just over five minutes remaining and Anders Lee scored on a power play late to put the game away.
Special teams proved to be the Lightning's unpinning on Monday. The Bolts were 0-for-3 on the power play, while the Islanders scored goals on the power play and shorthanded.
The Bolts are back in action tomorrow against the Panthers in Sunrise.
Scoring Summary
1st Period
No Scoring
2nd Period
NYI | 6:44 Ross Johnston (2) - Ryan Pulock
NYI | 8:37 Josh Bailey (8) - Casey Cizikas, Johnny Boychuk - SHG
TBL | 15:35 Steven Stamkos (10) - Kevin Shattenkirk, Anthony Cirelli
3rd Period
NYI | 7:31 Brock Nelson (10) - Unassisted
NYI | 14:41 Brock Nelson (11) - Anders Lee, Jordan Eberle
NYI | 16:05 Anders Lee (8) - Josh Bailey, Mathew Barzal - PPG