Shea Theodore had a goal and an assist for Vegas (24-9-1), which had its six-game home winning streak end. Marc-Andre Fleury made 26 saves.
"It was one of those nights," Golden Knights coach Peter DeBoer said. "You have to give them credit. They played with desperation that we didn't match.
Athanasiou scored his first goal in nine games at 1:58 of the first period to give the Kings a 1-0 lead. The Golden Knights allowed a goal in the first two minutes for a third consecutive game.
"We emphasize a good start every night," Vegas captain Mark Stone said. "The last three haven't been good, but at the same time, there's points in a game where we can get back into it. Tonight, we fell a little too far"
Lias Andersson, playing his first NHL game since Feb. 16, made it 2-0 at 17:23 of the first.
"Every game is huge at this point," Andersson said. "It's a tight league and a lot of good teams. We treat every game as a playoff game now. [We] don't get too stressed about the standings, just trying to take it one game at a time."