Rice led 62-58 with 1:51 left in overtime. Then Brandan Walton hit a 3-pointer on North Texas' next possession. Rice missed four-straight free throws and Jones made both of his with 11 seconds left. Marcus Jackson missed a shot at the buzzer.
Walton scored 17 for North Texas (16-15) and Jordan Williams added 11 and 14 rebounds.
North Texas closed regulation on a 7-0 run, with a Walton 3-pointer, a Williams layup and two Jones free throws with 23 seconds left. Rice's Keith Washington missed a game-winning shot.
Rice (7-23) was led by Austin Ramljak with 17 points, Sean Obi's 12 and Seth Gearhart's 11.
North Texas will play No. 7 seed Tulane Wednesday.