Toronto dominated the first half and Sebastian Giovinco came close to scoring after just five minutes.
Jozy Altidore gave Toronto the lead on the verge of half time with his 13th goal of the season.
Didier Drogba was a man on a mission in the second half, and single-handedly turned the match on its head.
First, the former Chelsea striker hit the woodwork from 10 yards in the 50th minute. He then scored two goals in 60 seconds to give Montreal the lead and become the club's leading scorer this season.
Michael Bradley was denied by the crossbar in the 79th minute with his powerful effort from 10 yards as Toronto slipped to sixth place in the Eastern Conference.
The two teams will meet again in Quebec next week in the playoffs knockout round.