Fiala, who leads Los Angeles with 72 points (23 goals, 49 assists) this season, returned after missing a 2-0 loss at the Edmonton Oilers on Thursday with a lower-body injury.
"When he gets on the ice, he forgets about it," said linemate Alex Iafallo, who had two assists. "It's good to see him grind through that. He had a huge game for us. It doesn't affect him, he's still making plays and controlling the puck."
Pheonix Copley made 25 saves for the Kings (44-22-10), who had lost two in a row.
Los Angeles remains one point behind the Edmonton Oilers for second place in the Pacific Division, and three points behind the Vegas Golden Knights for first. The Oilers defeated the Anaheim Ducks 6-0 on Saturday, and Vegas defeated the Minnesota Wild 4-1.
"Down the stretch, they're going to be tight games and they're going to be hard-fought battles," Copley said. "That's how we wanted to play defensively. We were shutting things down, keeping it to the outside, and that was really good to see."
Oliver Bjorkstrand scored, and Martin Jones made 16 saves for the Kraken (41-26-8), who have alternated wins and losses for eight straight games (4-3-1).
"Both teams checked really well," Jones said. "It's that time of year, teams are ramping up for the playoffs, and there's just not a lot of room out there. … Neither team was really able to break free and make a lot of plays offensively."
Seattle remained three points ahead of the Winnipeg Jets for the first wild card into the Stanley Cup Playoffs from the Western Conference.
"It's a real disappointing loss, but in saying that, this group knows what it takes," Kraken coach Dave Hakstol said. "In the first two periods, we didn't win enough of those first pucks to give ourselves an offensive opportunity in the O-zone."
Sean Durzi put Los Angeles ahead 1-0 at 11:45 of the second period. He fell down after knocking the puck around the boards but got back up just in time to tap in the puck into an empty net after Iafallo's shot attempt from the slot deflected to him off the stick of Jared McCann.
"That was a lucky bounce, but sometimes you need those," Iaffalo said. "Sometimes they don't go your way, but you'll take the ones that do."