Gabriel Vilardi had a goal and an assist, Kevin Fiala had three assists, and Jonathan Quick made 27 saves for the Kings (6-5-0), who have won two straight and three of four.
"It has been that way for a couple of nights," Los Angeles coach Todd McLellan said. "We'll see what happens in Dallas (on Tuesday). We knew we'd have our hands full. Obviously, they're not very happy with their game, just as we were a few games ago (in a 6-4 loss to the Winnipeg Jets on Thursday). I like the way we started, and we stuck with it. I think we checked our way to some goals, which was really important. Then down the stretch, the penalty kill came up right big. I thought 'Quicky' had a real good night. Overall, a real good night."
The Blues (3-5-0) have been outscored 25-8 during their losing streak. Jordan Binnington allowed five goals on 19 shots before being replaced by Thomas Greiss, who stopped all 11 shots he faced.
"I can say it and [the fans] can see it, it's kind of a [pathetic] effort from us the last couple games," St. Louis defenseman Justin Faulk said. "We have leads, we're down one today going into the second period and just kind of lay an egg. There's no reason for it. The other team's trying to win, and if you can give them an inch, they can tell, and obviously Montreal saw it the other night (in a 7-4 loss on Saturday). They saw we sat back and didn't want to play a hard game, and they took it over. L.A. did the same thing here."
Vilardi gave the Kings a 1-0 lead at 13:12 of the first, redirecting a backdoor cross-ice pass from Fiala near the right post during a delayed penalty.
It was Vilardi's eighth goal of the season, which is tied for second in the NHL. Edmonton Oilers center Connor McDavid leads with nine.