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.
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.