Kasperi Kapanen cut it to 6-5 from the right circle at 8:11, but Drew Doughty scored 39 seconds later from the right point on a power play to give the Kings a 7-5 lead.
Los Angeles was 4-for-5 on the power play. St. Louis was 2-for-2.
"You got to win in different ways even when you're not playing your best, which was evident tonight," McLellan said. "The power play came through."
Kyrou made it 7-6 at 19:11 with Binnington pulled for the extra skater.
"Not really into consolation prizes. We were down 5-1," Faulk said. "Generally with three, four-goal games, the other team sits back and the team starts to get chances. It happens the other way, too. … It made it more fun to play than down 5-1 the whole way, that's for sure."
NOTES: Fiala had two assists in his return after missing six games because of a lower-body injury. … Arvidsson has seven points (five goals, two assists) in his past three games. … Kempe has scored an NHL career-high 36 goals in 73 games this season. He had 35 goals in 78 games last season. … Doughty has scored in three straight games and has five goals in his past six. He had three goals in his first 66 games this season.