Tulane's Chris Moore had a chance to win the game with a long try with six seconds remaining but the attempt missed and the Ponies put the game in the win column.
Tulane's record falls to 8-9 overall, and 1-4 in C-USA action.
SMU is now 12-7 overall and 1-4 in C-USA. The victory broke a four-game losing streak for the Ponies.
SMU was led by Ike Ofoegbu, who scored a game-high 19 points. Jon Killen added 12 points and grabbed seven rebounds for the Mustangs.
Tulane's defense held SMU to 28.6 percent shooting from the field in the first half, and 30 percent from the floor for the game, as the Green Wave took a 30-22 lead into the locker room at halftme, and stretched their lead to as many as 13 in the second half.
In the second half SMU rallied on 16-of-18 shooting from the free throw line to stake themselves to the two-point victory. For the game the Ponies made 19-of-24 free throw attempts.
Tulane continued it's season-long offensive struggles as the Wave shot just 35 percent from the floor, and were even worse from beyond the three-point arc, making only 4-of-16 shots from outside.
The Green Wave shooting woes worsened in the latter stags of the second half, and Tulane managed to score only 7 points in the final seven minutes of the game, and were held scoreless from the floor for six minutes in that stretch.
The unusual disparity between Tulane free throw attempts and their opponents attemptd from the charity stripe continued as SMU had 24 chances to Tulane's 13. Over the past three games, Tulane has shot just 48 times from the free throw line, compared to their opponents 77 free throw attempts.
Tulane returns to action Saturday night at Fogleman Arena when they continue C-USA action with a contest against Rice. Tipoff is set for 7 p.m.