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.
The second annual Gavitt Tipoff Games, eight games between members of the Big East and Big Ten to be played Nov. 14-18, will feature Villanova at Purdue in the opener.
Michael Lewis is leaving his assistant coaching job at Butler to take the same position at Nebraska under Tim Miles.
College basketball fans should be excited about next season's Jimmy V Classic, an event that will feature Duke's heralded freshman class.