Cal Clutterbuck scored for the Islanders, who have lost Game 3 at home in each of the first three rounds of the playoffs. Semyon Varlamov made 23 saves.
Teams that take a 2-1 lead are 89-25 (.781) winning a best-of-7 NHL semifinal series. Game 4 will be played here Saturday (8 p.m. ET; USA, CBC, SN, TVAS).
"They've been in this position a few times, obviously, they're Stanley Cup champions," New York coach Barry Trotz said. "They've been in these situations. We tried. We have to get more pucks, we're going to have to get inside. We had some chances, and Vasilevskiy made a couple of key saves.
"They didn't have a lot tonight. I thought we were pretty good defensively as well. A lot of stuff they got, I think we gave it to them. It's funny, as you go along this path deeper and deeper, these teams are better and better, and you've got to dig in even harder and harder."
Kyle Palmieri had a chance to give New York an early lead, but Vasilevskiy got his glove on his shot from point-blank range at 6:53 of the first period.
Yanni Gourde then gave Tampa Bay a 1-0 lead at 10:05, quickly shooting the puck from a sharp angle after Blake Coleman's centering attempt from below the goal line redirected to him off the skate of Islanders defenseman Nick Leddy.