Alex Iafallo scored, Gabirel Vilardi had an assist to extend his point streak to four games, and Cal Petersen made 17 saves the Kings (21-26-7), who lost their last four home games (0-3-1).
Los Angeles was 9-14-5 at home this season.
"We have work to do," Kings coach Todd McLellan said. "Our younger players that have been in the League now for a year or two must show improvement. They have to begin to carry more of the load, offensively, defensively, game management. It's a must that they graduate and move on to the next level, break through."
Bozak beat Petersen between the pads with a backhand in the slot to put the Blues ahead 1-0 1:25 into the third period. Faulk had an assist, his 200th in the NHL.
Iafallo scored his 13th goal on a one-timer from Vilardi to tie it 1-1 at 7:35. Vilardi has five points (three goals, two assists) during his streak.
"I'm feeling comfortable right now," Vilardi said. "I'm playing with two good linemates that both work hard, and I'm able to get the puck so I can make more plays. We're creating right now offensively."