Lawson Crouse and Jack McBain scored, and Karel Vejmelka made 15 saves for Utah (34-30-12), which has lost four of its past six games.
Utah is nine points behind the Minnesota Wild for the second wild card into the Stanley Cup Playoffs from the Western Conference with six games remaining.
“There's a few broken plays that made the difference in the game, but I think the guys were ready and we were really structured,” Utah coach Andre Tourigny said. “We didn't give up much. Unfortunately, a few breakdowns made the difference.”
Fiala put Los Angeles ahead 2-1 at 4:06 of the third when he intercepted a cross-ice pass from John Marino in front of the net and lifted a quick shot over Vejmelka’s glove.
Moore then pushed it to 3-1 on a breakaway at 4:50.
"[Phillip Danault] just made a really good play, knocking it out of the air,” Moore said of his goal, where he picked up a deflected puck in Utah’s zone and beat Vejmelka. “Those fluky things happen from time to time. We'll take them.”
Doughty scored an empty-net goal to make it 4-1 at 18:10.
McBain drove to the net and scored with his backhand on the power play for the 4-2 final at 19:40.
The Kings were outshot 16-3 in the first period, but Kuemper made all 16 saves to keep the game scoreless.
“He just made good saves and he's done that for us all year,” Kings head coach Jim Hiller said. “We knew he was a good goalie and he was going to play well for us, but he's been our backbone all year. In wins like this, you just need your goaltender to let you get your legs underneath it, and he gave us every opportunity. Otherwise, it should have been over early, and we would not have been able to come back. Give him full marks.”