Brayden Point had a goal and two assists, and Nikita Kucherov had a goal and an assist for the Lightning (45-26-6), who have won three in a row after losing their previous four.
Tampa Bay remained four points behind the Toronto Maple Leafs, who have two games in hand, for second in the Atlantic Division. The Maple Leafs won 3-0 at the Ottawa Senators on Saturday.
"We're starting to find a little identity with our team, and we've played some really good teams," Lightning coach Jon Cooper said. "Don't get me wrong, this score is not indicative of the team we just played. We're playing playoff teams. We've got through Boston (2-1 loss on March 25) and Carolina (4-0 win on March 28) and now the Islanders, and yeah we didn't win them all, but we've been pretty darn competitive in them."
Ilya Sorokin allowed four goals on 21 shots before being pulled in the second period for the Islanders (39-29-9), who had won two straight. Semyon Varlamov made 10 saves in relief.
New York is two points ahead of the Florida Panthers and three ahead of the Pittsburgh Penguins for the first wild card into the playoffs from the Eastern Conference.
"Overall, we had some breakdowns, a couple of mistakes, a couple of bad bounces, but it is what it is," Islanders forward Kyle Palmieri said. "I mean 5-0, 10-0, 1-0 … we're going to reset and try to win a hockey game tomorrow (at the Carolina Hurricanes)."