The lead changed hands 13 times in the first half until Marshall's Ryan Taylor made a layup with 41 seconds to play to tie the score at 27.
UTEP opened the second half with a 10-0 run, then pulled away to lead by 17 on a Matt Willms dunk with 11 minutes left. Marshall came back and made it a five-point game on a layup by Chris Thomas, but Hunter kept it out of reach with a free throw and a dunk with 10 seconds to go to give UTEP a 10-point advantage.
Julian Washburn scored 17 and UTEP (11-6, 1-1) outshot Marshall (6-11, 1-1) 46.8 percent to 31.7 percent.
Taylor led Marshall with 18 and Chris Thomas scored 13.
Mike Brey is looking at former Notre Dame players to fill two assistant jobs that have opened up with the departures of Martin Ingelsby and Anthony Solomon.
Purdue's 2016-17 prospects got a jolt Wednesday when forward Caleb Swanigan announced he will return for his sophomore season.
Clemson's Jaron Blossomgame says he is withdrawing from the NBA draft and returning to school for a final season.