Leading 44-40 early in the second half, Manhattan (4-2, 1-0) went on a 30-13 run to take a 74-53 lead with 4:11 left. Austin and Smith each had seven points during the decisive run.
The Golden Griffins (3-4, 0-1) never got closer than 15 the rest of the way.
Darryl Crawford added 16 points for Manhattan, who shot 11-of-22) from 3-point range.
Manhattan has beaten Canisius in 12 of the team's last 14 meetings.
It was the Jaspers' fourth-straight MAAC-opening win and seventh in the last eight years.