Adrian Kempe had two goals and an assist, and Pheonix Copley made 28 saves for the Kings (24-14-6), who have won three of four. Anze Kopitar had an assist for his 1,100th NHL point, becoming the third player in Los Angeles history to reach the milestone.
Stuart Skinner allowed three goals on 24 shots before being replaced by Jack Campbell, who made 11 saves for the Oilers (21-18-3), who have lost four of five (1-3-1).
Edmonton, who has the best power play in the NHL (31.0 percent), finished 0-for-6 with the man-advantage.
"I thought there were some very good looks that we got to, and we weren't sharp enough on our offensive opportunities, and that's going to happen some nights," Oilers coach Jay Woodcroft said. "Our power play has operated at the level it has this season, it's going to happen. How about the penalty kill step up and take care of the other team's power play? If that would have happened, I think we wouldn't be talking about our lack of production."
Fiala gave the Kings a 1-0 lead at 9:21 of the first period on a power play. He scored on a one-timer from the right circle off a pass from Kempe.
Fiala then made it 2-0 with another power-play goal 1:50 later. He stole the puck from Brett Kulak along the boards, skated toward the net and scored short side on Skinner.
"We wanted to win the special teams battle, and when you do against that team, you give yourselves a much better chance at success," Kings coach Todd McLellan said. "If you would have told me at the beginning of the night it would have been 4-0 in our favor, I'm not sure I would have agreed with you, considering we had 12 minutes of penalty kill. It's not a recipe for success against that team. Rarely are they going to be shut out in that type of situation, so we were fortunate to come through it tonight."