Bradley opened the scoring in the 35th minute with his fourth goal of the season. Altidore connected in the 55th, hammering in a rebound for his 10th goal after Jonathan Osorio hit the post. Altidore has three goals in the last two games, all coming off the bench.
Former Toronto striker Dominic Oduro scored for Montreal in the 74th minute.
Toronto won 11 games last year and has nine games left — seven at home — as its pushes for a first playoff berth.
Montreal fired coach Frank Klopas early Sunday and said assistant Mauro Biello will take over on an interim basis.
The 48-year-old Klopas was in his second season with Montreal after coaching the Chicago Fire from 2011-13.
In Chester, Pennsylvania, Uruguay's Diego Fagundez became the youngest player to score 25 MLS goals as the New England Revolution beat the Philadelphia Union 1-0 for their third straight victory.
Fagundez, who is 20 years, 6 months, 15 days old, signed with the Revolution on Nov. 15, 2010, and is in his fifth MLS season.
The Revolution scored in the 51st minute when Charlie Davies flicked a pass to Fagundez, who drove to the top of the area and cut it back inside the left post.
The Columbus Crew beat New York City 2-1 to move into second place in the Eastern Conference after Justin Meram scored in the 83rd minute.
Federico Higuain opened the scoring with a hard-bouncing header off Wil Trapp's corner in the 10th minute. Andrew Jacobson equalized for City in the 20th minute with a long strike.
Houston's Ricardo Clark and Raul Rodriguez scored to give the Dynamo a 2-0 win over Vancouver to end a three-game winless streak, while Kevin Doyle broke a deadlock in the 76th minute as the Colorado Rapids held on to beat Sporting Kansas City 2-1 for its third straight victory.
In other games, Orlando City capitalized on a Chicago Fire own goal to earn a 1-1 draw and FC Dallas' Tesho Akindele and Fabian Castillo scored in a 2-0 victory over Real Salt Lake.