Leissner scored seven points during an 11-0 run to give New Hampshire a 44-34 lead with 8:04 left. Maine pulled within 58-56 with 23 seconds to go, but the Wildcats hit 5 of 6 free throws to seal it.
Jaleen Smith had 14 points and Matt Miller added 10 for the Wildcats, who have won four straight and six of their past seven games since snapping a five-game losing skid.
Kevin Little scored 22 points to lead Maine (2-19, 1-7). Shaun Lawton chipped in 12 for the Black Bears.