McElroy completed 17-of-25 passes for 219 yards while Richardson had five catches for 101 yards, 11 rushes for 45 and three kickoff returns for 74 yards to help the Crimson Tide (6-1, 3-1 SEC) rebound from an upset loss to South Carolina last weekend that snapped their 19-game win streak.
Ole Miss (3-3, 1-2) was hampered by 12 penalties for 106 yards and Rebels quarterback Jeremiah Masoli connected on just 18-of-40 passes for 110 yards with one touchdown and an interception.
Ole Miss has won just once in 34 games at Alabama.
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