Copley said he has been putting in extra work with goalie coach Mike Buckley before and after practice to correct an inconsistent start to the season. Prior to Saturday, he was 2-0-2 with a 3.75 goals-against average and .845 save percentage backing up Cam Talbot (10-3-1, 2.02 GAA, .931 save percentage).
"It's been helping me out a lot," Copley said. "The guys are playing great in front of me, so that helps a lot. The extra work has been just sharpening things up."
Moore scored on a wraparound to extend the lead to 2-0 at 9:55 of the second.
The Kings made it 3-0 at 3:14 of the third when Jaret Anderson-Dolan stole a pass in the Canadiens zone and fed Trevor Lewis, who scored with a wrist shot from the bottom of the right circle.
"They give you no room to breathe," Allen said of Los Angeles. "When you have time and space against those guys, it's totally different than you would against another team. They play probably the best team game I've seen in the League ... It's really impressive to watch."
St. Louis said the Kings benefit from having all the players on the ice working and skating hard, whether they have the puck or not.
"That's what we're chasing, that's what we want to look like," St. Louis said. "When we do that, we're hard to play against. We've just got to find more consistency and play with that pace when we lose pucks."
Moore made it 4-0 at 13:26, scoring his team-leading 11th goal of the season with a backhand from just above the goal line that slipped through on the short side. Moore has six points (four goals, two assists) in his past three games.
"We stuck with our game," Moore said. "A couple turnovers there in the second, but other than that, it was shift after shift doing what we wanted to do, staying patient and we got the win."
NOTES: The Kings had never shut out the Canadiens in Los Angeles in 76 previous games. ... The Kings are 11-0-1 when scoring first this season. ... Dubois has eight points (two goals, six assists) in his past five games against Montreal.