The Green Wave's record rises to 17-12 overall. Tulsa's record falls to 20-11 overall.
Tulane, which struggled offensively although the Wave shot 42 percent from the floor for the night, was led by freshman guard Kevin Sims who scored 15 points to lead all scorers.
Sims was 5-of-10 from the field, and 2-of-3 from the free throw line. In addition, Sims hit on 3-of-5 attempts from three-point range.
Andrew Garcia, who was 2-of-2 from the floor, and 1-of-4 from the line for 5 points, grabbed 6 rebounds to lead Tulane in that category.
The Hurricane held Tulane's Chris Moore, who averages 10.6 points a game, to only 3 points in 28 minutes of action.
Tulsa was led by Jamel McLean, who scored a team-high 13 points on 5-of-7 shooting from the floor. McLean was also Tulsa's leading rebounder with 11.
The only other Hurricane in double figures was Charles Ramsdell with 11 points.
In the first half, Tulane connected on 46 percent of their shots from the floor on a 13-of-28 shooting performance. The Wave took a 31-23 lead into the locker room at the half.
The Wave's offensive woes showed in the team's shooting percentage from beyond the arc, with the Wave going 3-of-13 for a 23 percent three-point shooting percentage.
And the Green Wave shot only 54 percent from the free throw line, on a 15-of-28 performance.
In the first half, the Green Wave never trailed although the Hurricanes tied the score at 2-2, and 6-6. The Wave led by as many as 11 but took an 8-point lead, 31-23, into the halftime locker room. Both teams played sluggish basketball in the early going and with 8:30 remaining the Wave led by the anemic score of 13-10.
David Gomez led Tulane in the first half with 9 points on 4-of-7 shooting from the floor.
Kevin Sims hit a pair of treys and scored 8 points on 3-of-5 shooting. In the first half, Sims was 2-of-2 from beyond the arc.
Senior Kory Castine was 3-of-3 from the floor in the first half, and scored 7 points in five minutes of action.
Andrew Garcia was 2-of-2 from the floor, led the team in rebounding with 4, and also contributed 3 assists and a pair of steals to the Green Wave cause.
Overall, the Wave was 2-of-8 from beyond the three-point arc in the first half.
Castine and Gomez both attempted three free throws in the opening period, making one each. As a team, Tulane was only 3-of-8 from the line for the half.
Tulsa rallied in the early going in the second half and cut the Tulane lead to one at 34-33 on a Jamel McLean layup with 15:15 remaining. But the Green Wave outscored the Hurricane 8-4 over the next three-and-a-half minutes but couldn't shake Tulsa.
Tulane led 41-35 at the 12:57 mark after a Robinson Louisme layup, but Tulsa went on an 8-1 run to take a 43-42 lead on a Rod Earls' jumper. It was the Hurricane's only lead of the evening.
The Wave got the lead back on baskets by Daniel Puckett and Kevin Sims.
The Hurricane pulled even at 47 on a McLean layup with 5:29 remaining. The tie didn't last long as 16 seconds later Donnie Stith made a lay in and the Green Wave went back up by 2.
But the Green Wave couldn't shake off the Hurricane, and Tulsa pulled back into a tie at 51 with 3:46 remaining when McLean completed an old fashioned three-point play. But that tie didn't last long either and the Greenies took the lead again 18 seconds later when Chris Moore drained three free throws after being fouled by Tulsa's Rod Earls to put Tulane up 54-51. The points were Moore's first of the evening.
Tulsa's defense stymied the Wave for the next 2:51, and Brett McDade made a layup to cut the Tulane lead to 1 at 54-53 with 1:06 left in the game.
Tulane's Robinson Louisme scored on a layup with :37 remaining to put the Wave back up by 3. Both Earls and McDade missed treys for the Hurricane on the ensuing possession, and Kevin Sims snatched the rebound of McDade's shot but was fouled by Tulsa's Calvin Walls. Sims missed the free throw, but was fouled by Darold Crow with 13 seconds remaining. Sims drained both of those free throws and the Wave led by 5 at 58-53.
Tulsa's Charles Ramsdell drained a trey with 6 seconds left on the clock to make it a 2 point game at 58-56. Tulane's Asim McQueen was fouled on the inbounds play and had an opportunity to ice the game. But McQueen missed both free throws, and Ramsdell rebounded for the Hurricane with 4 ticks left and the game was still on the line. But as the fates would have it, Tulsa was unable to get off a shot before the final horn sounded.
Tulane will be in action again Friday at 8 p.m., when they face tournament host Memphis in the tournament semifinals. Memphis, the regular season conference champ and No. 1 seed, defeated Marshall Thursday 92-71.