Puriefoy was 7 of 13 from the floor with three 3-pointers and 10 of 13 from the line. Stony Brook (14-8, 5-2 America East) was 9 of 20 beyond the arc.
Binghamton erased a six-point halftime deficit and took a 46-45 lead on Willie Rodriguez's layup with 5:57 left.
But the Seawolves responded, going on a 14-2 run - 12 of which came from Purifoy - to put it out of reach.
Binghamton (2-20, 1-6 American East) was led by Marlon Beck II with 15 points. Rodriguez finished with 10.