The Green Wave's record is 2-0. Charleston Southern's record falls to 1-1.
Robinson Louisme scored 7 points on 3-of-3 hooting and led the team with 8 boards.
The Wave was 23-of-46 from the floor, excellent shooting on the road, while holding the Bucs to 38.6% from the floor overall.
The Buccaneers stayed close because they were 11-of-23 from beyond the arc, while Tulane made 7-of-16 treys.
Tulane led by as many as 11 points late in the second half, but but Charleston Southern rallied to cut the Green Wave lead to 3 points in the final minute.
Tulane returns to Fogleman Arena Friday for a game with the Nicholls State Colonels. Tipoff time is 7:05 p.m.