Copley is 2-0-0 with a 2.00 goals-against average and .927 save percentage since being recalled from Ontario of the American Hockey League on Dec. 1.
"It was kind of a weird game," Copley said. "There were a lot of blocks where I wasn't getting a lot of work, so it was kind of more one of the games where you have to be mentally sharp. The guys were doing a really good job with puck possession and playing in the other end. … The guys battled hard, and it was a good win for us."
Anze Kopitar and Viktor Arvidsson scored 19 seconds apart in the first period for Los Angeles (15-11-4), which was coming off a 5-0 loss at the Toronto Maple Leafs on Thursday.
"Good response by the group as a whole," Kings coach Todd McLellan said. "Whether you were an eight, nine-minute man tonight or a 20-minute man, you were responsible for your game. I think we came to the rink and we trusted each other tonight. We didn't do that in Toronto, and it showed on the ice."
Mike Hoffman and Cole Caufield scored, and Jake Allen made 31 saves for Montreal (13-12-2), which has lost three of four (1-2-1).
"They're a well-structured team, we all know that," Allen said. "I think they're a good hockey club. I know we don't see them often, but they've got some good veterans, some good chemistry over there, and I think their neutral zone is tough to crack. That 1-3-1 forecheck is tough to crack, and they're good at possessing the puck in the O-zone. We saw that tonight, creating chances from that."