The loss eliminated Montreal (3-12) from playoff contention and guaranteed the Hamilton Tiger-Cats a playoff berth in the CFL East.
Bo Levi Mitchell completed 20-of-34 passes for 199 yards and three interceptions as Calgary (12-2) extended its winning run to three games.
It was the first time this season that Mitchell failed to throw a touchdown pass.
Johnny Manziel, who's still looking for his first CFL victory, went 18 for 29 for 250 yards and an interception for his best offensive performance of the season. Boris Bede kicked two field goals for the Alouettes.
Montreal has now failed to make the playoffs for a franchise-record four consecutive seasons. The Alouettes have not made the post-season since 2014.
(The Canadian Press)