Mason's 1-yard plunge early in the fourth quarter handed Auburn a 10-point lead and he later capped the scoring with a 13-yard scoring run for the Tigers (12-1, 7-1 SEC), who rolled up 677 yards of total offense.
Mason carried the ball 46 times in setting the record for most rushing yards in an SEC title game.
Nick Marshall completed 9-of-11 passes for 132 yards with a score and also ran 16 times for 101 yards and a touchdown.
Sammie Coates hauled in six passes for 94 yards, including a 38-yard a scoring strike in the first quarter as the Tigers kept their hopes for a national championship alive.
James Franklin went 21-of-37 for 303 passing yards with three TDs and an interception for Missouri (11-2, 7-1).
Henry Josey rambled for 123 yards on nine carries.