The Golden Hurricane (17-11, 10-4 Conference USA) led 37-30 at halftime and outplayed Tulane (15-13, 3-11) in the final minute to win.
Ricky Tarrant and Jordan Callahan scored 21 and 16 points respectively for the Green Wave.
A foul shot apiece by Tre Drye and Tarrant put Tulane up 65-63. Clarkson, though, stuck a 3-pointer and Idlet answered Drye's layup with a jumper to make it 68-67. Tarrant's basket gave Tulane its last lead, 69-68.
Haralson's jumper with 35 seconds remaining regained the lead, and McClellan's two free throws with 17 seconds clinched it.
Tulsa outscored Tulane 40-22 in the paint.