The Wildcats (9-19, 5-11 America East Conference) trailed 72-69 with 2 minutes left, but got a 3-pointer from Chandler Rhoads and a jumper from Chris Matagrano to take a 74-72 lead.
Mike Allison responded with a tying layup for Maine (11-18, 6-10) with 47 seconds left, only to have UNH pull back ahead behind Myrick’s two foul shots.
The Black Bears missed a pair of 3-pointers in the final 20 seconds while the Wildcats added three more free throws for the five-point margin.
Rhoads and Patrick Konan each finished with 13 points.
Justin Edwards hit 9 of 9 foul shots and finished with 29 points for Maine. Alasdair Fraser added 22 points and Allison grabbed 12 boards.