After trailing by double figures in the first half, Southern Miss (6-12, 3-4 Conference USA) broke it open midway through the second half with a 13-2 run to make it 55-45 with 5:33 left. Jackson scored 11 in the run, which gave the Golden Eagles the lead for good.
Quinton Campbell added 13 points and nine rebounds, Robert Thomas III scored 12 and Khari Price 10 for Southern Miss, which hit just 33 percent from the field but made 12 3s and went 23 for 29 from the foul line.
UTEP (11-10, 3-5) raced to a 17-3 lead in the first half and carried a 30-26 advantage into the break.
Lee Moore led UTEP with 18 points and Earvin Morris, who fouled out, had 13.