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.
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Will Grier threw four touchdown passes to four receivers -- all in the first half -- and No. 25 Florida downed third-ranked Mississippi 38-10 on Saturday night.
Leonard Fournette highlighted his SEC-record third straight 200-yard game with a 75-yard touchdown run, and No. 9 LSU overcame Eastern Michigan 44-22 on Saturday night.
An officiating error led to an Oklahoma State touchdown Saturday in the Cowboys' 36-34 win over Kansas State.
Texas A&M receiver Ricky Seals-Jones, who was ejected for targeting midway in the second quarter of Saturday's game, took to Twitter late in the game, retweeting a tweet that questioned the call.
Florida State running back Dalvin Cook exited in the first quarter of the Seminoles' 24-16 win over Wake Forest with a left hamstring injury. He is day-to-day.
As if things weren't going bad enough at Texas, the Longhorns appear to have players on Twitter during lopsided losses and jabs at their coach accidentally being sent from other nearby teams.