D'Andre Wright added 12 points for the Golden Hurricanes (15-5, 8-0 American Conference), who have now won 10 straight games.
Tulsa ended the first half on an 8-0 and took a 27-20 lead at the break. They extended their lead to as many as 16 in the second period before Tulane (13-8, 4-5) made a late comeback bid that ultimately fell short.
Payton Henson led Tulane with 12 points and five rebounds off the bench. Louis Dabney added 11 points.
The win improves Tulsa to 13-0 this season when holding opponents to fewer than 65 points. Its 8-0 start in conference play is the school's best start since 1984-85, when it also opened league play 8-0.