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.
Colorado State graduate transfer John Gillon has chosen Syracuse, giving the Orange a potential starter at point guard entering the 2016-17 season.
DeSean Murray, who averaged 20.2 points as a sophomore at Presbyterian, will transfer to Auburn to play for coach Bruce Pearl.
Former Kentucky guard Ed Davender, the only Wildcat with at least 1,500 points and 400 assists, has died. He was 49.