Mathew Barzal scored for the Islanders (21-15-2), who had their three-game winning streak end. Ilya Sorokin made 31 saves.
"We weren't clean on our breakout," New York coach Lane Lambert said. "You can't play with speed if you can't execute or exit your zone cleanly, and we didn't do that. Give them credit, they had good gaps all night and we didn't execute the way we wanted to, and when we did have the puck in the neutral zone at times, we turned it over instead of getting it deep and establishing our forecheck."
Adam Larsson gave Seattle a 1-0 lead at 9:53 of the first period when he pinched in and scored with a one-timer off a pass from Ryan Donato, who had curled out from below the goal line.
"They wanted us to compete more," Kraken forward Oliver Bjorkstrand said. "Have better awareness out there, how we need to reload and coming back and finding that balance between offense and defense. I thought we executed better"
Barzal tied it 1-1 at 17:30, sneaking a shot five-hole on Jones from in front after receiving a return pass from Casey Cizikas. It was Barzal's fourth goal in his past three games.
"That wasn't great, not a lot of possession," Barzal said. "A lot of errors and some ugly hockey out there. Fast game, played up-tempo. Seemed like they came at us in waves all night."
Tolvanen, who was claimed off waivers from the Nashville Predators on Dec. 12, put Seattle back in front 2-1 at 3:58 of the second period with a one-timer from the top of the right circle on a power play.
"It felt really good," Tolvanen said "It's been a while since I played my last game (Nov. 19), so it's nice to get the first goal out of the way in the first game. … It's just the power play. Before we go we're talking about just getting pucks on net and shooting it right away when we got it in zone."
