Albany (18-8 12-1) had a chance to tie at the end but the Stony Brook defense forced Evan Singletary to take a deep 3-point shot with five seconds left. He was off the mark and Warney pulled down the rebound to secure the win.
Albany led through most of the second half until Scott King's layup at the 9:38 mark started a 14-4 run to give Stony Brook (18-10, 9-4) a 55-49 advantage with 3:51 left.
Singletary hit a jumper and made two free throws to close to 57-56 with 1:24 left. Carson Puriefoy, who finished with 15 points, made two late free throws for the win.