Just two days on from scoring a hat-trick in a 5-1 win over the Vegas Golden Knights, Fiala finished with two power-play goals and two assists to improve the Kings to a 2-0-0 head-to-head record against the Oilers this season.
It was the sixth game this campaign in which Fiala finished with at least three points, and McLellan was effusive in his praise of the left winger.
"His engine is really good, he can play lots of minutes, he's dangerous and he can play up and down the lineup," McLellan said after the Kings' victory on their home rink at the Crypto.com Arena.
"His game transfers with him wherever he goes. He can play with big players, small players, quick, crafty players, straight-line players. It's rare to find a player like that."
Adrian Kempe had two power-play goals, making it the first instance the Kings had two players doing so in one game, while Alex Iafallo and Viktor Arvidsson registered goals for in-form LA, who have gone 9-2-1 since the middle of December.
McLellan acknowledged his side were fortunate not to be punished more.
"It's not a recipe for success against that team," he said. "Rarely are they going to be shut out in that type of situation.
"So we were fortunate to come through in that situation. I thought our penalty killers did a really good job."
The Kings, who had seven penalties in total to the Oilers' six, ultimately triumphed because of their proficiency with the power plays, Edmonton coach Jay Woodcroft felt.
The Oilers have given up 42 power-play goals this season, tied most with the Anaheim Ducks.
"I think the refs got involved. There was a lot of calls both ways and we went 0-for-6 on our power play and they scored four on their power play, four on seven," Woodcroft said.
"So obviously some of those penalties are within our control and our penalty kill. They moved the puck around well and give them a little bit of credit, but our penalty kill can be a lot sharper and we ended up on the wrong side of the special teams battle.
"I thought that was the difference in the game."
The Kings sit second in the Pacific Division of the Western Conference, with the Oilers down in fifth.