Perreault put the Jets ahead 2-1 at 1:16 with a backhand shot past Carey Price from the slot.
"I didn't even really see it," Perreault said. "I saw the replay and it was an awesome pass. Honestly, it came to me and I just whacked it in."
Laine scored his 28th goal into an empty net with 1:17 remaining.
Connor Hellebuyck made 19 saves for Winnipeg (27-29-5), which has five points in its past three games (2-0-1) after losing four straight.
"It's a continuation," Jets coach Paul Maurice. "We've had three really, really strong games, and more of the same tonight. They're almost identical games that we've played, really strong with our gap, not giving the other team a whole lot, and getting enough offense. The time of year says you're probably not going to see the 7-6 games anymore and you're going to get into the 2-1 games, and we were comfortable with that."
Price made 30 saves for Montreal (31-20-8), which extended its losing streak to three in its first game since changing coaches during its five-day break.
"It wasn't a strong game," Pacioretty said. "We got outplayed, especially I feel in our end, and that was tough to create anything off of that offensively."
Julien signed a five-year contract to replace Therrien, who was fired after Montreal went 1-5-1 in the seven games preceding its five-day break. Julien first replaced Therrien during the 2002-03 season.
"I'm trying to learn as much about this team as I can in a short period of time because of where we are in the schedule and then where we are in the season," Julien said.