Peter Hooley added 15 for the Great Danes, including a 3-pointer with 1:04 remaining to put his team up 61-56.
Albany managed to pull out the road win despite losing Sam Rowley, who scored a game-high 18 points, when he fouled out with 7:02 left. Down six at the time, the Great Danes outscored Stony Brook 23-8 en route to their fourth America East Conference title.
Carson Puriefoy led the way for Stony Brook with 13 points, while Jameel Warney added 12.
The Seawolves were attempting to earn their first NCAA Tournament berth. They've lost three conference finals in the past five years.
Albany led 34-31 at halftime, and Rowley finished 9 for 11 from the field before fouling out. Albany coach Will Brown took a chance by putting the junior back in at the 7:38 mark. Eighteen seconds later, he drew his fifth foul while fighting for a rebound with Stony Brook's Eric McAlister.
Albany rallied to pull even at 52-52, and Hooley's 3-pointer helped seal the win.