Trailing 50-34 at halftime, Loyola pulled within 67-61 on a pair of free throws by Andre Walker with 9:28 to play. But Adams hit a 3-pointer to cap a 10-5 run to give the Bonnies a 77-66 lead with 5:20 left.
Loyola led early, but Idris Taggee's jumper sparked an 11-4 run for a 19-13 lead. Posley later scored 12 straight for St. Bonaventure - on back-to-back 3-pointers, four free throws and a jumper - and the Bonnies led by 16.
Tyler Hubbard led the Greyhounds (1-3) with 21 points on 7-of-11 shooting from long distance. Andre Walker added 14.