Kopitar pushed it to 5-3 at 10:39 when he scored from in close off a centering pass from Alex Turcotte.
Kopitar leads the Kings with 37 points (10 goals, 27 assists) in 32 games, and at age 37 his average of 1.16 points per game is the best of his 19-season NHL career.
"To be his age and to be out there playing against the other team's best players night after night, and then making an offensive contribution too, while leading the team, that's really difficult to do," Hiller said. "I know that. It's difficult to do it at 25, never mind at 37."
Quinton Byfield's empty-net goal at 16:23 made it 6-3, and Fiala closed the scoring at 17:34, scoring off a behind-the-back pass from Alex Laferriere.
The Kings felt the push at the end was needed after they couldn't build on a third-period lead in a 3-2 overtime loss at the Pittsburgh Penguins on Tuesday.
"I didn't think that Pittsburgh game was to our standard," Foegele said. "We have a high standard, and we keep everyone accountable. Third periods are something we take a lot of pride in. And in that Pittsburgh game, the third period, we let it slip. Tonight, we knew 20 minutes to go, play the right way, Kings hockey, and that's what we did."