Omega Harris finished with 23 points and 5 rebounds and Matt Willms chipped in with 14 points and 8 rebounds as the Miners improved to 5-4 in Conference USA action.
It was slow going for both teams in the opening minutes, but it was especially slow for the Miners who managed just four points in the first eight minutes of the contest, falling behind 11-4 early on.
Six straight by the Miners would cut into the Blazer lead and UTEP would manage to stay within striking distance for the remainder of the half, trailing 28-19 as the teams headed for the locker rooms.
UAB would strike first out of the break to extend their lead into double digits at 30-19, but the Miners would turn it on from there behind strong efforts from Harris and Willms.
UTEP would use a quick 10-0 run to cut the Blazer lead to one just four minutes into the second half, but UAB would respond with six straight of their own to get the lead back to seven at 36-29 with 14:08 to play.
Omega Harris would spark his team again though, scoring eight of nine Miner points over a five minute stretch, eventually tying the game at 38 with just over nine minutes left.
Harris and Willms would continue their assault on the Blazers, eventually capping a 37-16 second half run that turned a 30-19 deficit into a 56-46 lead.
The Blazers would hang around, thanks almost single handedly to Hakeem Baxter, as they would get the difference back to as few as three in the closing seconds.
However, it would be senior leader Dominic Artis who would knock down one of two free throws with seven seconds remaining, giving the Miners a two possession lead and sealing their 63-59 victory.
Omega Harris led the way for the Miners with a game high 23 points to go along with 5 rebounds and 2 assists. Matt Willms finished with 14 points and 8 rebounds, and Dominic Artis filled the stat sheet with 11 points, 8 assists, 5 rebounds and 5 steals.
Hakeem Baxter was the leading scorer for the Blazers, finishing with 12 points and 2 rebounds. Tosin Mehiniti was the only other Blazer in double figures as he went for 11 points and 6 rebounds.
The Miners finished the night shooting 45.8% from the field, while holding UAB to just 39.3%. Neither team was extremely effective from 3 point land (28.6%-30%) or the free throw line (50%-60%), but the Miners did make six more free throws than the Blazers.
UAB outrebounded UTEP 39-32, but it was the Miners who finished with 15 assists to just 12 for the Blazers while turning the ball over just 10 times, compared to 13 for UAB.
The win brings the Miners to 7-14 overall, but more importantly 5-4 in Conference USA, and give them 5 wins in their last 6 contests. UAB falls to 14-9, 7-3.
The Miners will next be in action Saturday night in the Don Haskins Center against league leading Middle Tennessee. That game is slated for a 6 pm tip.