Tulsa finished the regular season tied with Southern Miss, Louisiana Tech and Middle Tennessee atop the conference standings.
Shaquille Harrison added 15 points and Rashad Smith 14 for Tulsa (18-12, 13-3). The Golden Hurricane pulled away down the stretch, using a 6-0 spurt to break a tie at 54 for a 60-54 lead with 7:59 left.
North Texas (15-15, 6-10) closed to within 61-59 on Brandan Walton's free throws, but Harrison responded with a pair of free throws and Ray's basket with 3:29 left stretched the lead to 65-59.
Tulsa hit 10 of 12 free throws over the final 3:11 to preserve the win.
Walton and Alzee Williams each scored 20 points to lead North Texas.