Kofi Opare's 68th-minute strike was all that was needed for Bruce Arena's men to clinch victory at the StubHub Centre, which condemns the visitors to their sixth game without a win and stalling their playoff challenge.
However, the best effort of the first period was that of Gyasi Zardes, who weaved his way into the box and hit the outside of the post with a shot.
After the break, the Galaxy started to look more comfortable, and 23-year-old Canadian Opare made the most of a goal-mouth scramble to put his team in front with just over 20 minutes remaining.
The Canadian team tried to get men forward but ended up leaving themselves open at the back, although the home side could not add to their lead before the full-time whistle.
As things stand, Montreal are still just inside the playoff spots in the Eastern Conference, but are level on 46 points with Chicago Fire and Philadelphia Union, who are in fifth and sixth respectively.