Brayden Point scored for a fifth straight game, and Nikita Kucherov had three assists for the Lightning, who have not lost consecutive games in the Stanley Cup Playoffs since the 2019 Eastern Conference First Round (12-0). Andrei Vasilevskiy made 24 saves.
"We've got good leadership in our room, and they keep our team from getting too high or too low," Point said. " … I don't know, it's tough to put a finger on it really. It's gone good so far, but we can't be happy with just this one. It's going to be a hard, long series. We've got to look at the next one."
Brock Nelson scored, and Semyon Varlamov made 23 saves for the Islanders, who won their previous four games. Ilya Sorokin made six saves in the first period after Varlamov missed the final 6:50 following a collision with Point.
Game 3 of the best-of-7 series is at New York on Thursday.
"We knew they were going to come with a good response after we got the first game," Nelson said. "I thought we did a pretty good job coming out of the gates 1-1, but it's hockey. Bounces, breaks, whatever it may be, they were able to get a couple and get the lead, and we weren't able to get it back."
Ondrej Palat gave Tampa Bay a 2-1 lead at 13:15 of the second period. Victor Hedman sent a stretch pass to Kucherov, who drew two defenders in the left face-off circle before sending a pass into the slot to Palat for his first goal in nine games.
"Obviously, you guys know there was too many men on the ice," Islanders coach Barry Trotz said. "They had seven guys, so disappointed at that. But we tried to battle through that."