Evan Singletary gave Albany a 64-63 lead on a layup with 3:40 left, but the Great Danes were held scoreless the rest of the way. BU's Kyle Foreman stole the ball from Singletary and finished the fastbreak layup.
Peter Hooley missed a game-tying 3-pointer with 22 seconds left and Papale hit two free throws to seal it.
Nathan Dieudonne and Foreman added 15 points apiece for BU (1-1). Foreman also had seven rebounds and five assists.
BU made 10 3-pointers, while Albany struggled from distance on 1-of-13 shooting.