The Islanders (8-5-2, 30 points) won their fifth straight and third in a row.
They also defeated the New Jersey Devils (6-6-2.
29 points) and Carolina Hurricanes (6.5-6, 20 points) for their fifth consecutive win.
The Islanders led 3-0 early in the third period and then held on for the victory.
“It was good to get out there, get out on the ice, get some wins, and see what the coaches are expecting of us,” said forward Jannik Hansen, who scored his first NHL goal.
Hansen had a goal and an assist.
Forward Matt Martin scored his second of the season for the Islanders, who are 12-0-2 in their past 17 games.
They are 4-0 since the beginning of March.
Martin, who had a career-high eight assists on Sunday, was a minus-3 in his past five games.
This is the first time the Islanders have won consecutive games since Jan. 14-16, 2000.
They have not lost consecutive games in their last nine contests.
Center John Tavares had a season-high four assists and two goals for the Devils, who have won three in a span of nine games.
Defenseman Derek Stepan had three assists and three penalty minutes.
He has one goal and two assists in his last three games.
Center Ryan McDonagh had four assists in 10 games.