The Blues, who had won eight of their previous nine games, missed a chance to move into a tie with Chicago at the top of the Central Division.
St. Louis had averaged three goals a game in their last dozen contests, but managed only a lone second-period goal from T.J. Oshie. That goal came on a penalty shot and created a 1-1 tie heading into the third.
King gave Los Angeles the lead 2:04 into the third, Trevor Lewis scored shorthanded less than three minutes later and Jeff Carter added an empty-net goal with 56 seconds left.
Jonathan Quick stopped 28-of-29 shots for the Kings, who have allowed the fewest number of goals (98) in the NHL this season.
Jaroslav Halak made 27 saves for the Blues.
The game ended with a melee touched off by the Kings' Jake Muzzin and the Blues' Vladimir Sobotka. They both received roughing penalties, but Chris Stewart of St. Louis entered the fray and wound up with slashing and game misconduct penalties.