Leissner made two layups in the extra period, the second giving the Wildcats a 66-63 lead with 2:47 remaining. Binghamton's Romello Walker made a free throw, then Matt Miller answered with a jumper and the Wildcats shot 5 of 6 from the line to seal it.
Miller finished with 16 points and Leissner grabbed nine rebounds to lead New Hampshire (9-9, 2-3 America East).
Binghamton (2-18, 1-4) had the final possession with 12.4 seconds left in regulation. Justin McFadden missed a falling, one-handed jumper in the lane at the buzzer, but didn't draw the foul after an officials' review to send it to overtime.
Walker scored 11 of his 12 points in the second half, and McFadden had 12 to lead the Bearcats.