Grice carried the ball 24 times and scored on two 1-yard runs in the first half as the Sun Devils (8-2, 6-1 Pac-12) took advantage of five turnovers to move one game ahead of UCLA and Southern California for first place in the Pac-12 South.
Arizona State next plays the Bruins at Pasadena, Calif.
Jaelen Strong ran for 106 yards and Taylor Kelly went 22-of-37 through the air for 183 yards with two interceptions as ASU won a fifth straight.
Sean Mannion was picked off four times for the Beavers (6-4, 4-3), completing 31-of-46 passes for 320 yards with two touchdowns.
Swim Week Miami Beach 2014 [PHOTOS]