Albany improved to 11-7 overall with the win, and 4-2 in the America East. Stony Brook fell to 6-11 overall and 1-4 in conference play.
The Great Danes went on a 14-5 run to open the second half in building a 38-28 lead. Jimmie Covington scored seven of his 11 points in that burst.
But Albany responded with 14 of the game's next 18 points. Jamar Wilson, who had eight points of the game, had six consecutive free throws to ignite the run.
Stony Brook fought back over the next seven minutes behind the play of Ricky Lucas, who had 13 of his 17 points after halftime. Lucas sank two free throws to slice the deficit to four, including 61-57, with 1:49 remaining.
Stony Brook shot 37.9 percent from the field for the game.