Matty Beniers and Alex Wennberg also scored power-play goals, and Grubauer made 20 saves for the Kraken (6-8-4), who had lost three in a row (0-2-1) and four of their previous five games (1-2-2).
Seattle lost 4-3 in overtime at the Edmonton Oilers on Wednesday after letting a two-goal lead slip away in the third period.
“Coming out of last night, that was a disappointing loss,” Kraken coach Dave Hakstol said. “We felt like we did so many really good things there. But you know, true to the group in here, we addressed a couple of things that we felt like we could do better, and then we said, ‘Let's turn the page.’”
Varlamov made 29 saves, and Mathew Barzal had two assists for the Islanders (5-6-5), who are 0-4-3 and have allowed 12 power-play goals in 24 chances during the skid, including three in four Thursday.
“It was a special teams battle,” New York captain Anders Lee said. “I mean, a lot of penalties on both sides, good road game by us, up-and-down hockey. They transition well. They've done that the last few years, so no different tonight.
“We never throw up our hands. It’s frustrating, for sure. But there's no quit in this team, there's no quit in the group. That's why we're playing good hockey; it's just not getting the results.”