The Bulldogs (6-4, 3-3 SEC) became bowl-eligible with their second straight win over a ranked opponent.
Alabama (6-4, 4-3) lost its second straight game, following a setback last week against second-ranked LSU.
Alabama quarterback John Parker Wilson completed only 16-of-34 passes for 121 yards and had two interceptions.
Alabama held a 9-3 lead and was threatening at the Mississippi State two-yard line with 21 seconds to play in the first half. Wilson's pass was picked off at the goal line by Johnson, who raced virtually untouched to score with just four seconds to play.