Dixon led the Bulldogs (1-1) with 80 yards on 18 carries. Mississippi State rushed 46 times for 216 yards, while the Lions (1-1) gained only 33 yards on the ground.
Carroll redeemed himself with 158 yards passing after tossing three interceptions in Mississippi State's 22-14 loss to Louisiana Tech last weekend.
Bulldog wide receiver Brandon McRae set a season and game highs with eight catches for 72 yards, including one touchdown in the third quarter.
Adam Carlson hit a pair of second quarter field goals for the Bulldogs. Austin Wilbanks had a 1-yard touchdown catch to give Mississippi State a 20-3 lead in the second quarter.
The Mississippi State defense had five sacks.