Thomas was 9-of-15 shooting and grabbed nine rebounds, while Black contributed 10 points and 13 rebounds. Joe Jackson added 17 points and five assists for the Tigers (12-3, 2-0).
Rod Rucker paced the Blazers (8-9, 0-2) with 16 points and 11 rebounds for his seventh double-double this season and third straight. The junior is averaging 17.7 points and 13.3 rebounds over his past three contests.
Memphis dominated on the glass with a 44-34 rebounding advantage.
Both teams struggled beyond the arc, with Memphis connecting on 1 of 12 attempts and UAB going 0 for 13.
Memphis led 19-17 when D.J. Stephens' layup sparked a 15-3 run that put the Tigers up 34-20 at the intermission. Memphis maintained the double-digit lead the rest of the game.