SMU (3-3) shot 52 percent from the floor, including 7 of 14 from beyond the arc, where Moore was 3 of 4. Keith Frazier added 16 points and Yanick Moreira had 15 points and seven boards.
Texas Southern (0-5) was led by Madarious Gibbs with 16 points and nine assists. Chris Thomas and Deverell Biggs both added 11 points for the Tigers, while Malcolm Riley had 10 points.
SMU led by just one after 10 minutes but went on a 16-2 run, punctuated by Moore's 3-pointer, and led 32-25 at the break.
A 10-2 run at the start of the second half, capped by Frazier's trey, pushed the lead into double figures and SMU cruised from there.