McCarron connected on 16-of-23 pass attempts for 208 yards before leaving the game in the fourth quarter with a bruise on his upper back.
The Crimson Tide (8-0, 5-0 SEC) got rushing touchdowns from T.J. Yeldon and Kenyan Drake.
Mississippi State (7-1, 3-1), meanwhile, couldn't prevent its nine-game win streak from being snapped as Tyler Russell was held to 169 yards with an interception on 15-of-30 efficiency.
Chris Smith made three grabs for 73 yards for the Bulldogs.
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