Stark, Tulane's leading scorer last season at 14.5 per game, entered the contest averaging just 7.3.
Tre Drye also scored 14 for Tulane (3-1) and Jay Hook made all nine of his free throws on the way to 12 points. Payton Henson came off the bench to score 11 points.
Southern (1-4) was led by Trelun Banks with 15 points. Cameron Monroe had 11 points and three steals, and Joell Hopkins added 10 points.
Banks made two consecutive baskets to pull Southern within 70-57 with 2:03 left, but Hook and Drye made 4 of 4 free throws the rest of the way to seal it.
Tulane led by double-digits the entire second half.