Richards hit a 3-pointer to give Manhattan a 59-58 lead, then neither team scored for almost three minutes until RaShawn Stores' 3-pointer extended the lead to 62-58 with 2:47 left.
Canisius went scoreless in the final 2 minutes, including Zach Lewis' missed 3-pointer in the final seconds.
Rich Williams added 12 points for Manhattan (5-8, 2-2 Metro Atlantic Athletic Conference). The Jaspers led 34-31 at halftime after shooting 58 percent from the field.
Crumpton hit a 3-pointer to cap a 9-2 run for a 55-54 lead with 7:30 left, but Canisius only made two field goals the rest of the way.
It was the 85th all-time meeting between the two programs.