The Aggies (8-0), who never trailed in the game, extended the one-point halftime lead of 30-29 to as much as 12 in the second half. The Aggies started the second half with a 12-5 run and held Auburn (5-3) without a field goal for more than six minutes.
A&M held an eight-point lead over the Tigers with 47 seconds to play before Auburn's pressure quickly narrowed it to four.
The Aggies got two free throws from both Chris Walker and Marlon Pompey in the last 25 seconds to seal the win.
Acie Law added 19 points on the night and Kenneth White scored a career-high 10.
Auburn got double-digit point totals from four players, led by Frank Tolbert's 15 and Ronny LeMelle's 14.
Sophomore guard Tolbert was 5-of-9 from the field. LeMelle, a senior guard from River Falls, hit back to back 3-pointers to close the gap in the second half. Quantez Robertson posted 10 points and led the team in assists with six. Rasheem Barrett added 10 points and pulled down a team-high six rebounds for Auburn. Josh Dollard also grabbed six rebounds.
Auburn outrebounded Texas A&M 33-28. The Tigers were 6-of-22 from 3-point territory.