Phillip Danault scored, and Cal Petersen made 19 saves for the Kings (34-22-8).
"Little details I think was the big difference," Danault said. "We played a decent game, but those mistakes we've got to make sure [aren't] as big as the ones we gave up."
Evgenii Dadonov gave the Golden Knights a 1-0 lead at 18:19 of the first period when he collected his own rebound at the right side of the net and scored on a wraparound.
Chandler Stephenson pushed the lead to 2-0 at 39 seconds of the second period with a power-play goal. He took a cross-ice pass from Eichel and beat Petersen above his right shoulder for his 15th goal, setting an NHL career high.
"I didn't have to do anything, just put my stick there," Stephenson said. "That's the kind of player [Eichel] is. He's an All-Star. You can be anywhere. Even if there are three guys, four guys in front of you, he seems to be finding you. His game seems to keep getting better and better.
"It's fun to watch."