Ivan Barbashev, Ryan O'Reilly and James Neal also scored for the Blues. Jordan Binnington made 32 saves as St. Louis won its fourth straight game to open a season for the third time in franchise history.
Perron's sixth career hat trick gave him five goals in his last two games.
"I think everyone's pulling on the rope," Perron said. "We're all trying to keep getting better."
Alex Iafallo, Justin Brown and Carl Grundstrom scored for the Kings, who lost their fourth straight. Calvin Petersen made 33 saves.
Iafallo's first goal of the season, off a rebound from an Alexander Edler shot, gave the Kings a 1-0 lead with 8:31 left in the first period.
Iafallo almost had another goal late in the first, but Binnington got his right pad on a backhander on a partial breakaway.
Perron evened the game with a power-play goal with 5:34 left in the first. It was the first of four power play goals for the Blues, who went 4 for 7 with the man advantage.
St. Louis killed off all four of the Kings' power plays.
"I've felt we've been pretty good with the puck," said Blues defenseman Torey Krug, who had three assists. "Tonight, it obviously went in the net for us. We're a confident group right now."
Barbashev made it 2-1, scoring the Blues' first short-handed goal of the season with 1:13 left in the first. Marco Scandella started the play by forcing a turnover at center ice, leading to Barbashev's breakaway.
"When you're minus-5 in specialty situations it's not going good anywhere for you, and that's the worst I've seen us penalty kill maybe in the NHL since I've been here," Kings coach Todd McLellan said. "That was very disappointing. Our power play was just as bad."
Perron's second of the game came off a deflection of a shot by Krug 45 seconds into the second period.
Neighbours made it 4-1 a couple of minutes later, burying a perfect feed from Brayden Schenn.
"I didn't really have a picture in my head of what it was going to look like, but I was hoping it would come sooner rather than later," Neighbours said. "Just came off the bench and kind of jumped into the slot there. He put it right on my tape, not much I had to do."
O'Reilly's power-play goal gave St. Louis three goals on its first six shots of the second period. Neal scored another power-play goal, his first as a member of the Blues, in the third.
Perron completed the hat trick by burying a one-timer on the power play in the third.
"He wants to make plays, he wants the puck in big moments," Krug said of Perron. "So, you couple that with the high-end skill that he has, the pucks going to go in a lot of times for him."
Brown and Grundstrom scored third-period goals for Los Angeles. Anze Kopitar's four-game goal scoring streak was snapped.
"It's definitely not the game we wanted," Iafallo said. "We're embarrassed right now."
Blues LW Pavel Buchnevich served the second of a two-game suspension for a head butt against Arizona forward Lawson Crouse on Oct. 18. ... Kings D Drew Doughty was scratched. Doughty was injured after taking a knee-to-knee hit from Dallas D Jani Hakanpaa on Friday night. Doughty had tied the franchise record for most points through the first three games of a season for a defenseman, with seven points (1 goal, 6 assists). ... Blues LW Brandon Saad was scratched after being placed in COVID-19 protocol. ... Kings D Olli Maatta made his season debut.
The game was the first of two straight the Kings will play at St. Louis. The rematch is Monday night at Enterprise Center.