Quinnipiac led 56-48 with 12:03 to play before BU used a 15-7 run to tie it at 63. The Bobcats led 68-66 with 3:11 remaining, but committed two turnovers and missed two field goals down the stretch.
Nathan Dieudonne made a pair of free throws to tie it at 68 with 2:01 to go before Papale drained the game winner.
Cedric Hankerson scored 23 points on 7-of-13 shooting from the field, and had five steals and seven rebounds to lead BU. Papale finished with 13 points.