Johnson stepped in for injured Nick Marshall and went 10-of-16 through the air for 192 yards with an interception as the Tigers (7-1) built up a 38-0 lead.
Marshall ran six times for 73 yards with a touchdown before exiting with a shoulder injury sustained during a sack.
Sammie Coates hauled in Johnson's first pass for a 36-yard touchdown and later added a 67-yard score for Auburn.
Cameron Artis-Payne led the Tigers' ground game, picking up 93 yards with a touchdown on 13 carries.
The Owls (2-6) got 192 yards of total offense from quarterback Jaquez Johnson in their fourth loss in five games.