The Golden Hurricane were dealt a 75-72 loss to the Green Wave at Devlin Fieldhouse in New Orleans.
James Woodard led TU with 21 points, Pat Swilling Jr. scored 13, Shaquille Harrison scored 11 and Scottie Haralson logged 10.
Tulsa shot 47 percent (27-of-57) for the game, 32 percent (6-of-19) in 3-pointers and 67 percent (12-of-18) in free throws.
Ricky Tallant led Tulane with 21 points. Josh Davis scored 19 and 11 rebounds for a double-double and Kendall Timmons got 10.
The Green Wave shot 43 percent (21-of-49), 39 percent (10-of-26) in 3s and 79 percent (23-of-29) from free throws.
Despite losing, Tulsa out-boarded Tulane, 37-29.
TU trailed 29-16 with 4:42 left in the first half, but drew within 36-30 before halftime.
A lay-up by Harrison tied the score at 61-61 with 5:09 to go, but Tarrant hit back-to-back 3-pointers.
Two free throws by Swilling drew TU to within 73-72 with 18 seconds left. But Davis countered with a pair from the foul line two ticks later. No more points would be made.
Tulsa continues on the road Wednesday night at Houston. Tipoff time is at 7 p.m.