Rice, which had won their previous two games in double overtime in putting together a three-game win streak, took their first lead since early in the game on Seth Gearhart's layup and Max Guercy added a 3-pointer with 2:02 left for a 56-52 lead. But Rodriguez connected two 3-pointers, the second with 24 seconds remaining, and Kris Gulley added two free throws while the Owls missed their final three attempts, all from the behind the arc.
Rodriguez finished 12 points, all on 3-pointers, and Adrian Diaz also scored 12 while Gulley added 11 for the Panthers (13-13, 6-7 Conference USA).
Gearhart had 13 points and a career-high tying 11 rebounds for his second-straight double-double. Marcus Jackson added 10 points for Rice (9-16, 6-7).