The shutout was Saros' 21st of his career.
"I feel good", he said. "I just try to keep building my game. In games, there's always something where you might be a little bit rusty in some situations, so I try to be the best I can. I take reminders of all of the situations that are going on, stay humble, and work hard."
Andrew Brunette, hired by Nashville on May 31, picked up his first win.
"It was really cool", he said. "The introductions and the start of the game reminded me of a different time when I was way younger and less gray. I got more gray as the game wore on.
"Once you're a player and you've put on a Predators uniform, even though you're not a player, you always feel like you're still a player. You still have all of the jitters and the excitement. It was fun to be a part of tonight for sure and to get a win makes it extra special."
Philipp Grubauer made 32 saves for Seattle, who were defeated 4-1 by Vegas in their season opener.
"[Grubauer] has been solid both nights here", said Kraken head coach Dave Hakstol. "He's given us good opportunities and has played very well. He's been sharp. He's seeing the puck well. I've really liked his competitive level. He played a good hockey game tonight."
Predators blank Kraken; Seattle drops to 0-2 to start the season
After a scoreless first period, Colton Sissons put Nashville in front 10:24 into the second, converting a shorthanded breakaway pass from Cole Smith and scoring on the backhand over Grubauer's blocker.
Gustav Nyquist doubled the Predators lead midway through the third period as his centering pass deflected off of the skate of Seattle defenseman Adam Larsson and in during a delayed penalty.
"I thought we did a good job of carrying the momentum and not giving it back to them too many times there", Nashville defenseman Ryan McDonagh said.
"We had to play a little patient game too. We did a lot better job not forcing plays and feeding their transition. That's a fast team over there with a lot of skill, so if you feed them with some turnovers, they can make you pay.
"But I think we learned some lessons playing [against Tampa Bay on Tuesday]. We stayed out of the box a lot better, managed the puck a lot better and you could see our forechecking game take over."
Jusso Parsinen scored into an empty net with 1:41 to play to complete the scoring.
"You try not to hurt yourself by taking penalties and turning pucks over", McDonagh said. "We talked about just staying within our structure, staying fast, being aggressive. When there's a play to be made, try to make it, but if not, just play a little bit more high percentage. You could see us doing that tonight, getting more [offensive] zone time with the forechecking game. It was a lot more fun to play tonight than the other night."
"It was a tight hockey game", Hakstol said. "The turning point at the middle of the game was giving up the short-handed goal. They took a lot of momentum out if that for the second half of the second period. In terms of, I wouldn't say 'chaotic' is the word, but on the offensive side, a few too many missed nets."