Manziel scored three times on the ground, finishing with 90 rushing yards on nine carries and added a pair of TD passes en route to 260 aerial yards for the Aggies (6-2, 3-2 SEC).
Ryan Swope made six grabs for 140 yards with two touchdowns as Texas Tech bounced back from a 24-19 loss to Louisiana State in its previous game.
Trey Williams led the Aggies' rushers with 109 yards and a score on 19 carries.
Auburn (1-7, 0-6), meanwhile, fell for the fifth straight time as Jonathan Wallace was held to 6-of-9 passing for 122 yards and two touchdowns.
Notable deaths of 2014 [PHOTOS]