David Perron scored his sixth NHL hat trick and had an assist for the Blues (4-0-0), who started a season with four straight wins for the first time since 2017-18.
"It's very special obviously after what we've been through the last while," Perron said. "It was a special night, it was great. We were able to kind of put behind a bit of a slow start, I'm not saying like crazy bad, but like a few minutes there and we were able to kind of turn the page quickly on that."
Torey Krug had three assists, Jake Neighbours scored his first NHL goal, and James Neal scored his first with the Blues in their home opener. Jordan Binnington, who has started each game for St. Louis, made 32 saves.
Alexander Edler had two assists for the Kings (1-3-1), who have not won since defeating the Vegas Golden Knights in their season opener Oct. 14. Cal Petersen allowed seven goals on 40 shots.
The Blues played without forwards Brandon Saad (NHL COVID-19 protocol), Pavel Buchnevich (suspension) and Oskar Sundqvist (knee).
"That was pretty clear evidence that we're a pretty deep team," Krug said. "When one guy goes out, the other guy steps in and does the job to the best of his abilities. We're great up front with that depth right now. Any line can do some damage. It's fun right now, it's rolling, and obviously we've got to continue to work at it."
St. Louis went 4-for-7 on the power play and outscored Los Angeles 5-0 on special teams.
"I think that set us up for the whole night. When you're minus-5 in special-teams situations, it's not going anywhere for you," Kings coach Todd McLellan said. "That's the worst I've seen us penalty kill, maybe in the NHL, since I've been here. That was very disappointing. Our power play was just as bad. So obviously your 5-on-5 game's not going to be very good when that's as bad as it is."
Los Angeles was without defenseman Drew Doughty, who sustained a lower-body injury in a knee-on-knee collision with Dallas Stars defenseman Jani Kahanpaa in the second period of a 3-2 overtime loss Friday. There was no update on Doughty's condition.
Alex Iafallo gave the Kings a 1-0 lead at 11:29 of the first period.