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.