After Golden's big return gave UTEP (3-8, 2-5 Conference USA) the 34-27 lead, the Golden Eagles (0-11, 0-7) responded with an 86-yard drive that cut the lead to one with 2:48 left.
Southern Miss coach Ellis Johnson opted for a two-point conversion attempt, but Arsenio Favor's pass was intercepted by Demarcus Kizzie in the end zone.
UTEP quarterback Blaire Sullivan finished with 155 yards on 9-of-15 passing and rushed for 98 yards and a score.
Nathan Jeffery added 76 yards on the ground, including touchdown runs of one and three yards in the second quarter.
Favor, the fourth Golden Eagles' quarterback to start in 2012, completed 16 of 22 attempts for a season-high 374 yards and two touchdowns.