Tyler Harris hit a 3-pointer to give Providence a 60-55 lead with 48 seconds to play. Evan Singletary answered with a 3 to pull Albany within 60-58 with 39 seconds left before Kris Dunn and Harris each made a pair of free throws to seal it.
Harris scored 18 of his 23 points in the second half. Kyron Cartwright dished out five assists and added eight points for the Friars.
The teams have faced each other just once before when Providence beat Albany in overtime, 31-30, in 1928.