Gallagher and Suzuki picked up assists on the goal.
The Habs headed to the room up 2-0 after 20 minutes, and limited the Golden Knights to that lone shot on goal while registering 20 of their own.
The Golden Knights got back into the game in the second. With Ben Chiarot in the box for delay of game, Alex Pietrangelo unleashed a one-timer which beat Jake Allen to cut the Habs' lead to one at the 5:16 mark.
Vegas would tie the game just over five minutes later, when Jonathan Marchessault found himself in perfect position to bury a rebound from in close for his fifth of the season to make it 2-2.
Just over 90 seconds later, on another power play, the Golden Knights took their first lead of the night when Dylan Coghlan wristed it through traffic to beat Allen and put the visitors ahead 3-2.
That's where things stood after two periods of play.
The third period remained a scoreless affair until late in the game. With a player from each side in the box with with under four minutes to play, the Habs pulled Allen in favor of an extra attacker, but Chandler Stephenson broke free and gave his team an insurance marker into the gaping net.
Brayden McNabb would add an empty-netter of his own in the final minute of play.
The Canadiens play again on Tuesday night, when the Los Angeles Kings are in town for their only visit to the Bell Centre of the season. For tickets to that game,
click here
.