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.
The back-and-forth history of Jimbo and Saban
Ahead of Saturday's matchup in Tuscaloosa, get an inside look at the back-and-forth history between Jimbo Fisher and Nick Saban.
Alabama's Bryce Young a game-time decision vs. Texas A&M, Nick Saban says
Alabama coach Nick Saban said there's no structural damage to quarterback Bryce Young's right throwing shoulder, but Saban said a final decision on Young's playing status for Saturday's game against Texas A&M might not come until pregame warmups.
Iowa visits Illinois in battle of Big Ten West contenders
Iowa (3-2, 1-1 Big Ten) at Illinois (4-1, 1-1), Saturday, 7:30 p.m. ET (Big Ten Network)
Revisiting the history behind the Saban-Fisher relationship
Ryan McGee details the relationship between coaches Nick Saban and Jimbo Fisher ahead of their matchup on Saturday.
Out of Pocket highlights South Carolina's Jackson
Out of Pocket's Alyssa Lang discusses the Gamecocks' Director of On-Campus Recruiting, Jessica Jackson, and details her importance.
No. 12 Oregon on 4-game win streak, travels to face Arizona
Arizona's Jayden de Laura had one of the best passing games in school history against one of the Pac-12's worst teams last week.