The Jets, who were without injured forwards Mark Scheifele and Blake Wheeler, are five points behind the Dallas Stars for the second wild card from the West.
"We're in desperation mode right now, and it would be no different if we were in a playoff series and we were going back to back," Winnipeg coach Dave Lowry said. "That was the conversation that we had and understanding that we have to win every game here and just take care of business each and every night."
Josh Anderson scored his 100th NHL goal, and Sam Montembeault made 31 saves for Montreal (20-42-11), which has lost six of eight (2-5-1).
"[Montembeault] made two or three saves where the shooters were probably expecting the puck to be in the back of the net," Canadiens forward Brendan Gallagher said. "He's battling, he's competing, he's worked hard all year and it hasn't been the easiest for him. But he's been giving us a chance every night, so he's been playing some really good hockey."