Five straight points by Reynolds sparked a 19-3 run that was punctuated by a Morgan 3 and gave the Green Wave a 28-13 lead with six minutes left in the first half. Southern Miss was scoreless for more than five minutes during that stretch.
Tulane took a 37-19 advantage into halftime and led by at least 18 throughout the second half.
Southern Miss (2-8) made just 15 of 48 (31.3 percent) field goals, including 5 of 24 from 3-point range, and 5 of 10 free throws.
Eddie Davis III led the Golden Eagles with 12 points.
Tulane outrebounded Southern Miss 50-26.