Gary Roberts scored the only goal of the game off a tip-in of a Steve Eminger shot for the Lightning, who snapped a four-game losing streak. Steven Stamkos had the other assist on the goal.
"It felt like another game, I try to be as calm as I can and just do my job," said McKenna, who was playing just the third game and second start of his young career. "The guys played great in front of me and that makes a load of difference."
Before the game, the Lightning dealt forward Jussi Jokinen to the Carolina Hurricanes in exchange for forward Wade Brookbank, defenseman Josef Melichar and a fourth-round pick in 2009.
Yann Danis made 27 saves in the loss for the Islanders, who have dropped two straight after a four-game winning streak.
"He played great," said Islanders head coach Scott Gordon about Danis. "In the first period he made some great saves and if we don't get that performance in the first period, then the second and third probably don't even matter."
The only goal of the game came with 6:26 to play. Eminger threw a shot on net from the right point that an Islander knocked down, but the player cleared it right back to Eminger, who again wristed a shot on net that Roberts tipped past Danis for a 1-0 lead.
The Islanders were unable to get much pressure in the Lightning end for the next several minutes and a penalty to Kyle Okposo with 2:34 to play followed by one from Richard park just 20 seconds later effectively killed any chance the team had to tie the game.
Danis was busy in the first period as he had to make 16 saves to keep the Lightning off the board, compared to just seven saves made by McKenna.
The second period was also scoreless as McKenna stopped nine shots while Danis stopped five shots.