Arthur Kaliyev and Rasmus Kupari each scored on the power play, Anze Kopitar and Matt Roy each had two assists, and the Kings won for the first time since their season opener. Cal Petersen made 26 saves.
Los Angeles was 3-for-5 on the power play after going 2-for-21 over the previous six games, and coach Todd McLellan said it made all the difference.
"It gave us a cushion. It gave us some comfort. It gave us confidence," McLellan said. "We've been waiting for that to happen."
Josh Anderson scored for the second straight game, but the Canadiens were unable to post consecutive wins for the first time this season. Jake Allen allowed five goals on 38 shots.
Montreal held a lengthy team meeting following the loss.
"It takes a certain level of compete, a certain level of work to win in this league every night. And right now, we're not willing to give that on a consistent basis. And our results show that," Canadiens defenceman Ben Chiarot said.
After scoring just six goals in the second period through seven games, Los Angeles got two against Montreal, with special teams putting them in front after being largely absent during the winless skid.
Kaliyev buried a powerful wrist shot from the left circle to put the Kings ahead 2-1 at 12:19. It was his second career goal and first on the power play.
Los Angeles carried the momentum into the third, with Kupari scoring for the second straight game to make it 3-1 1:53 into the period.
"And when you score like that on the power play, other parts of your game come along with it," McLellan said. "You get confident. I think that might have been the difference in the game tonight."
Iafallo extended the lead to 4-1 at 5:37, and he got the Kings' third power-play goal at 14:16.
It was the Kings' first game with multiple power-play goals since defeating Vegas on opening night. The difference, Iafallo said, came down to being willing to shoot.
"I feel like we've been working on it in practice, and it hasn't been going for us well in the last few games, but tonight, what we wanted to focus on was getting shots through, no matter where it's coming from," he said.
The Canadiens took a 1-0 lead at 18:22 of the first period on Anderson's wrist shot from the right circle, but the Kings tied it up at 1-all when Viktor Arvidsson beat Allen with a wrist shot from the right circle at 4:31.
"We don't seem to have the right response now, the right kind of fight back, and that's the biggest thing," said Chiarot, who scored with 2:20 remaining in the third to make it 5-2. "I mean, we had momentum kind of rolling in that game, and then it kind of flips on us. Bunch of penalties, obviously, but we have to be able to bounce back."
Canadiens F Tyler Toffoli played against the Kings for the first time after spending his first eight seasons in Los Angeles, where he was a key part of the 2014 Stanley Cup-winning team. Toffoli was recognized with a video tribute in the first period and received a round of applause when he was announced as a starter, but he said the welcome reception was spoiled by Montreal's poor showing.
"It was really nice," Toffoli said. "I spent a lot of good, good years here, and it's just unfortunate that it's washed away by a bad effort."
It was Kopitar's third multi-point game. The Kings captain had not collected a point in his previous three games. ... Kings D Olli Maatta got his 100th career assist. ... Kings F Lias Andersson made his season debut after missing the first seven games because of a groin injury. ... Kings F Brendan Lemieux returned after missing six games while in COVID-19 protocol.
Canadiens: Visit the Anaheim Ducks on Sunday.
Kings: Host the Buffalo Sabres on Sunday.