The Mustangs (5-4, 4-1 Conference USA) blocked three kicks. After Sterling Moore blocked one as time expired in the first half, Bryan McCann returned the ball 74 yards for a score, giving SMU a 21-20 halftime lead. McCann's score helped SMU erase a 13-point first-half deficit.
Defensive end Margus Hunt blocked an extra point attempt and a field goal attempt by Rice (0-9, 0-5).
McNeal scored on a 9-yard run in the fourth to give SMU a 31-20 lead. Rice narrowed the SMU lead to 31-28 with 1:47 left when Nick Fanuzzi threw a 4-yard touchdown pass to Toren Dixon and the Owls converted the 2-point conversion.
Mustang quarterback Kyle Padron finished 17 of 24 for 234 yards and one touchdown. Padron started his second consecutive game for the injured Bo Levi Mitchell. He's won both games.
SMU's Emmanuel Sanders led all receivers with 136 yards receiving on six receptions and one touchdown. Sanders also became the active leader among all Division I Football Bowl Subdivision players with 30 career receiving touchdowns, one ahead of Oklahoma State's Dez Bryant.
Fanuzzi completed 29 of 42 for 250 yards and three touchdowns. He threw first quarter touchdown passes of 33 and 11 yards to Patrick Randolph in the span of 1 minute, 15 seconds.
Charles Ross also scored for Rice with a 1-yard touchdown run in the second.
SMU needs one more victory to become bowl eligible. The Mustangs last appeared in a bowl in 1984.