The Kings have won back-to-back games to get to 40 points and enhance their playoff chances.
Los Angeles took a 2-1 lead into the third period, but Vladimir Tarasenko scored his second goal of the contest for the Blues 6:44 into the frame.
Mike Richards snapped the 2-2 tie with a wrist shot and Justin Williams added an empty-net goal with 1:16 to go.
Jonathan Quick made 20 saves for the Kings, who handed the Blues their third straight loss.
Jaroslav Halak surrendered three goals on 39 shots.