Siena held a 10-point lead with 2:57 left to play but the Bonnies made five 3-pointers - including one at the buzzer - to end the game. The Saints were up by 10 at the half and led by as many as 16 after the break.
Marquis Wright scored 15 points, Javion Ogunyemi added 13 and Rob Poole finished with 12 for the Saints (1-2). Siena shot just 24 of 61 (39.3 percent) from the field and was outrebounded by the Bonnies 52-32.
Andell Cumberbatch led St. Bonaventure (1-1) with 24 points and 11 rebounds, and Marcus Posley added 22 points. Cumberbatch and Posley combined to make 7 of the Bonnies' 8 3-pointers.