The Tigers (14-3, 4-0 Conference USA) used a 12-0 run midway through the first half to erase an early deficit and were never threatened in the second half.
Jeremy Hunt added 14 points for Memphis, while Willie Kemp had 12 going 4-of-7 from 3-point range.
Joey Dorsey had 12 rebounds for Memphis, while Antonio Anderson had a career-high nine assists.
Wen Mukubu led UAB (10-8, 2-2) with 18 points, including a four-point play midway through the second half. Lawrence Kinnard scored 13 points, while leading scorer Paul Delaney finished with 12, 5.6 under his season average.
Memphis played most of the game without leading scorer Chris Douglas-Roberts, who tried to play but went to the locker room early. He is still bothered from a sprained ankle suffered against Houston two games ago.