Mason rushed for 181 yards and McCalebb ran for 104 yards for the Tigers (3-8).
Auburn ran for a combined 341 rushing yards and finished with 512 total yards, as the Tigers picked up their third win of the season and posted their highest scoring total of the season. McCalebb finished with 142 all-purpose yards.
Mason's two first-quarter touchdown runs, including an 86-yard score, helped give Auburn a 21-0 lead at the end of the quarter, and a 35-0 lead by halftime.
Freshman quarterback Jonathan Wallace finished 10-of-18 for 171 yards passing and on touchdown for the Tigers.
Deaunte Mason went 17-of-28 passing for 186 yards and threw an interception for Alabama A&M (7-4) in the losing effort.
The Auburn defense held Alabama A&M to just 22 net rushing yards on the day, with senior Kaderius Lacey leading the way with 41 yards on 12 carries. Wide receiver Demario Ross led the Bulldogs in receiving with 57 yards on four catches.
Tre Mason's 86-yard touchdown run was the longest by an Auburn running back since Brent Fullwood scored from 88 yards out against Mississippi State in 1986. Auburn's first four touchdowns Saturday came on the ground, capped by a 3-yard touchdown run by fullback Jay Prosch in the second quarter.
Wallace connected with wide receiver Sammie Coates for a 9-yard touchdown pass with 0:23 remaining in the quarter to give to Tigers their 35-0 lead going into the halftime break.
Alabama A&M got on the board with a score on the opening drive of the second half, when Deaunte Mason punched in a 1-yard touchdown.
After another McCalebb score, the Bulldogs gave up a team safety when an errant snap went over punter Chance Wilson's head, and was batted through the end zone.
Auburn sophomore Trent Fisher returned an Alabama A&M interception 60 yards for a touchdown with just under three minutes to play to give the game its 51-7 final score.
The Tigers' 512 total yards were the most by an Auburn team since the Tigers' national championship team totaled 519 yards against Oregon in 2010.