Tarrant was 7-of-14 shooting and made 4 of 8 from 3-point range, while Callahan knocked down six treys in 12 attempts and hit 7 of 13 overall for the Green Wave (17-9, 5-6 Conference USA).
Tulane made 46.7 percent (14 of 30) from 3-point range, helping overcome a 31-22 disadvantage in rebounds.
SMU (13-13, 3-8) knocked down 56.3 percent (27 of 48) from the field, though it was just 2 of 6 from 3-point range. Every starter scored in double figures, led by Shawn Williams with 16 points. Nick Russell added 13, Jalen Jones and Ryan Manuel 12 and Cannen Cunningham 10.
The Mustangs pulled within 65-62 on Jones' layup with 3:29 left, but Tarrant responded with consecutive 3-pointers and Ben Cherry later added another in building the final cushion.
Maryland point guard Melo Trimble, considered a lock to leave the program before struggling in the second half last season, has withdrawn from the NBA draft and will return for his junior season.
Louisville's Chinanu Onuaku, who recently underwent a medical procedure to correct a heart rhythm issue detected during the combine, will keep his name in the NBA draft pool.
Andrew White III will return to the Nebraska men's basketball team next season after removing his name from the NBA draft.