After Tulane scored the opening basket, the Mustangs (11-11, 4-4 Conference USA) scored 21 of the next 23 points, with Dia getting nine and Williams eight, for a 21-4 lead with 10:49 left in the first half.
The Mustangs built a 24-point lead, 35-11, with 4:47 remaining in the half before Tulane (7-15, 2-7) closed the first 20 minutes on a 10-0 run to trail 35-21 at the break.
The Green Wave trailed 56-48 with 4:25 to play, but SMU scored the game's final 10 points. Tulane did not score a field goal in 11 attempts in the final 7:17.
Dia pulled down 16 rebounds, helping SMU to a 41-17 advantage on the boards.
Kendall Timmons scored 14 points to lead Tulane.