The Owls (7-15, 2-7 Conference USA) shot 46.7 percent from the field, with Austin Ramljak scoring 12 points and Keith Washington contributing 11.
North Texas (11-11, 2-6) was held to 26-of-68 shooting (38.2 percent). Alzee Williams finished with 18 points and Colin Voss had 11 with 10 rebounds.
Rice jumped ahead early as Obi hit a layup and sank a pair of free throws to make it 21-5 seven minutes into the first half. North Texas closed the first half on a 13-4 run, making it 37-31 at the break.