Yanni Gourde had a goal and an assist, and Chris Driedger made 19 saves for the Kraken (17-34-5), who won for the first time since Feb. 11.
"I thought our team played great defensively," Seattle coach Dave Hakstol said. "We did a real good job all throughout the game 5-on-5. Our penalty kill was outstanding (2-for-3) in front of [Driedger]."
Roman Josi had two assists to reach 501 NHL points, and Saros made 27 saves in his 200th NHL game for the Predators (30-20-4), who played for the first time since losing to the Tampa Bay Lightning 3-2 in the 2022 Navy Federal Credit Union NHL Stadium Series on Feb. 26.
"It was really two areas," Nashville coach John Hynes said. "Our execution with the puck wasn't as good as it needed to be throughout the game. And then without the puck, our attention to detail defensively was not at the level that needed to be."
Philip Tomasino gave Nashville a 1-0 lead at 13:13 of the first period when he crashed the net and got his stick on a pass by Michael McCarron from behind the goal line that deflected off Driedger's stick.
Matt Duchene extended the lead to 2-0 at 6:54 of the second period with a power-play goal off the rush.
Seattle scored three goals in a span of 2:39 to take a 3-2 lead.
"The game goes back and forth, teams have good rushes, and they are creating chances," Kraken forward Alex Wennberg said. "They scored a goal, but just to find a way to push back there, that's a huge part of the game, the shift after when they score. It's a great chance to make a statement, and you either push back or you're going to let them go. I feel like it's great for us to come back and have that push. You see the team after one good play, you see the other line come out afterward and you're feeding off each other, and that's how the team works and that's how you'll be successful."