Gavrikov played 16:13 in his debut with Los Angeles; Korpisalo backed up Copley.
"He's an energetic outgoing guy, so I think he fit our group right away, right off the bat. He's not sitting back and he's not shy, so he's got that going for him," Kings coach Todd McLellan said of Gavrikov.
Denis Gurianov scored his first goal with Montreal since being traded from the Dallas Stars on Sunday, and Jake Allen made 30 saves for the Canadiens (26-31-4), who had won three in a row.
"It's all part of the process here, to learn how to handle those situations," Allen said. "Hopefully the next time around, we handle them better. That's just the situation we're in right now, and so it was a good learning experience."
It was the fourth straight win at home for Los Angeles, which will play eight of its next nine games here.
"You want to build that confidence at home," Kings defenseman Sean Walker said. "We're home basically all of March, so that's going to be key for us. A lot of games we're gonna have to win down the stretch here."
Vilardi reached the 20-goal mark for the first time in his four-year NHL career to give Los Angeles a 2-1 lead at 7:27 of the third period.
Kopitar made it 3-1 at 8:30 on a wrist shot from the slot to give him five goals in his past two games. He scored four in a 6-5 win at the Winnipeg Jets on Tuesday. He has 15 points (nine goals, six assists) in 10 games since the All-Star break.
"It's going in for him," McLellan said of Kopitar. "He's shooting maybe a little bit more, but the line (Kopitar, Adrian Kempe and Quinton Byfield) has found a chemistry that works for all three of them. Not just for one or two guys, and when you find one that works for all three, it can be effective, and everybody gets pulled along."
