Manziel, the reigning Heisman Trophy winner, sat out the game's first two quarters as a result of an NCAA probe into a sports memorabilia violation.
But with the Aggies (1-0) clinging to a 28-21 lead at halftime, the sophomore signal-caller entered to throw three touchdown passes, including two to Mike Evans, completing 6-of-8 throws for 94 yards.
Evans finished with six catches for 84 yards and Tra Carson rushed for two scores in the win.
Backup Matt Joeckel was 14-of-19 for 190 passing yards and a touchdown.
Rice (0-1) was led by Charles Ross with 107 rushing yards and two touchdowns.