The home side took the lead in the fifth minute when Johan Venegas lined up a strike from distance, and his effort took a deflection off Steven Neumann to loop the ball over Bobby Shuttleworth and into the net.
Didier Drogba almost doubled his side's advantage when he turned on the edge of the box and blasted a shot towards goal, but his effort was tipped on to the bar by Shuttleworth.
In the second half, Montreal doubled their advantage as Drogba rifled a free kick towards the net, which took a deflection off Kelyn Rowe and wrong-footed Shuttleworth to find the bottom corner.
However, Montreal secured their win four minutes later when Drogba put a through-ball into the path of Dilly Duka, who kept his composure to slot the ball past Shuttleworth to earn the three points for the home side.
The Impact move to sixth in the Eastern Conference, while New England remain in second in the table.