SMU (9-6, 1-0 Conference USA) trailed 50-41 with 6:22 left and began its comeback.
Two 3-pointers by Robert Nyakundi, the second with 3:08 left, brought SMU within 52-51.
Tulsa (7-9, 0-2) had a 55-51 lead with 1:26 showing, and Landon Giles hit two free throws for SMU.
Nyakundi led SMU scorers with 14 points and Giles added 11. Jordan Clarkson topped Tulsa with 14 points and Scottie Haralson had 11.
SMU had a 19-4 scoring advantage off turnovers.
The Mustangs are back in action Wednesday, Jan. 11 when they host Rice at Moody Coliseum. Tipoff is set for 7:00 p.m.