Fiala shot into an open net from the right circle after receiving a pass from Phillip Danault, who got his own rebound after his initial chance was blocked by Philipp Kurashev.
"I feel like we had so many chances. Just didn't go our way," Fiala said. "Hit bars, posts. We had so many long offensive shifts where we couldn't connect, but we stuck together and kept going and kept going, and that's how it turns out."
Danault had a goal and an assist, and Jonathan Quick made 31 saves for the Kings (9-6-1), who have won three straight and are 5-1-1 in their past seven games.
"This is more Kings hockey right now," Danault said. "We're playing good defensively, which creates frustration with the other team, and we create some chances on our side, so that's Kings hockey right now."