Cornell scored the first five points of the second half to take a 38-36 lead, but Canisius (2-1) used a 19-4 run over the next six minutes to take control.
McMillan entered the game as the nation's leading scorer at 32 points per game and was held to half that number on 5-of-10 shooting. Bleeker was 5 of 7 from the field. Phil Valenti scored 15 points and had five rebounds and three assists.
Five players totaled three-plus assists as Canisius assisted on 19 of its 30 field goals.