The victory snapped a three-game losing streak for Binghamton (11-7, 4-2 America East).
Hartford led 27-19 at halftime, and the Hawks built the margin to 42-29 on a layup by Morgan Sabia with 11:49 left.
But Rivera led the Bearcats on a 12-point run to close the gap to a point.
Mayben hit a 3 to tie it at 46-all with 5:37 remaining and sank another from beyond the arc to put the Bearcats up 51-49 with 4:23 to go.
Rivera then converted a three-point play, drained a 3 and made two free throws to give Binghamton a 61-51 lead with 2:38 left.