Jeff Carter recorded the game-winning goal 0, at Staples Center.
After Mike Richards and T.J. Oshie both recorded goals in the second round, Dustin Brown and Jaden Schwartz were each denied in the third.
Carter then raced down the center of the ice and made a quick fake in the slot before slipping a shot in between the legs of Brian Elliot. Chris Stewart had a chance to keep the Blues alive, but his backhander hit the outside of the left post to seal the Kings' sixth straight win.
Jonathan Quick stopped all 35 shots he faced to earn his eighth shutout of the season. With the victory, Los Angeles jumped up to third place in the Western Conference, surpassing the Phoenix Coyotes for the top spot in the Pacific Division.
Elliot made 37 saves for his seventh shutout of the year, but the Blues still dropped their fourth game in five tries.