Jackson tallied five of the Tigers 15 steals, and Memphis (24-8) held UTEP to 34-percent shooting (17 of 50).
UTEP scored 10 of the game's first 12 points, before Memphis mounted its comeback.
Trailing 20-17 with 6:46 left, the Tigers finished the first half on a 14-6 run.
Leading 30-26 at halftime Memphis opened the second half with an 11-4 spurt and led 42-30 with 16:03 remaining on Ferrakohn Hall's free throws.
Black had 15 points and 13 rebounds for the top-seeded Tigers, who play in the semifinals Friday night. Memphis, which lost to UTEP 60-58 on Feb. 18 in the teams' only other meeting, has won five straight and 18 of its last 21.
John Bohannon led the eighth-seeded Miners (15-17) with 15 points.