Turner's 4-yard TD pass to Cole Hunt added to Hayden Tobola's 19-yard field goal and Rice led 10-0 after the third quarter.
Driphus Jackson scored on a 3-yard run early in the fourth quarter. He finished 14-of-22 for passing for 122 yards and an interception.
After Tobola's 23-yard field goal, Jowan Davis scored on an 11-yard run for Rice (5-7, 3-5 Conference USA), which posted 433 yards of total offense to 285 for Charlotte, including 307 on the ground.
Deadlocked with no scoring at the halftime, Rice missed a field goal and Charlotte failed on three.