Winnipeg went into the evening clinging to hopes of a playoff appearance, but those hopes were dashed when both the New York Rangers and Ottawa won overtime games earlier in the evening.
With their season headed for a conclusion no matter what the result turned out to be in Winnipeg, the Jets faded during the third period. Winnipeg became the first NHL team to conclude the regular campaign.
Montreal remained tied with Boston for first place in the Northeast Division at 61 points, but the Bruins have two games remaining while the Canadiens have only one left to play.
Gallagher created a 2-2 tie 2:07 into the third period and David Desharnais put Montreal in front on the power-play 6 minutes later. Max Pacioretty gave the Canadiens some insurance with 9:10 to go.
Montreal won for just the second time in seven games. Carey Price made 23 saves in the victory.
Ondrej Pavelec gave up the four goals on 30 shots.