Rookie Arber Xhekaj notably earned his first career NHL point on the play.
The Caps made it a new game seven minutes later when Conor Sheary buried a pass from Nick Jensen on the doorstep to tie things up 1-1 at 9:02.
Longueuil native Anthony Mantha gave Washington the lead with a precise shot from the circle at 11:43 before T.J. Oshie doubled it at 15:20 to end the period 3-1.
Montreal outshot Washington 9-3 in the final frame, but the score remained unchanged.
The Canadiens will be back in action on Monday, when they host the Pittsburgh Penguins at the Bell Centre.