Nelson Kaputo made back-to-back 3-pointers and the Bonnies led by 23 in the second half after Izaiah Brockington's 3-pointer with 15:25 to play. Jackson State (1-2) rallied and closed to 64-57 on Paris Collins' layup 3, but Mosely hit a 3 and two free throws and the Bonnies (1-1) led by double digits the rest of the way.
Ayeni's 3 capped the Bonnies' opening 11-0 run, but the Tigers closed to 23-21 on a Collins 3. Mobley hit a 3 to spark a 10-0 run and St. Bonaventure led 39-26 at halftime behind Mobley's 18 points.
Jeremiah Jefferson scored 13 points and Collins finished with 10 for the Tigers.