The Aggies, who won their 23rd consecutive home game, improved their record to 9-1. Auburn fell to 9-1.
Sophomore forward Jordan Greenleaf led the Tigers with 13 points and nine rebounds. Whitney Boddie scored 12 points for Auburn. Boddie had six rebounds, five assists and five turnovers.
Junior Takia Starks led the Aggies with 17 points and Danielle Gant added 16 for the home team.
After trailing by as many as nine points in the second half, the Tigers pulled within a point with 3:17 remaining, 57-56, but senior point guard A'Quonesia Franklin scored A&M's next five points on a three-pointer at the shot clock buzzer and two free throws to spark the Aggies to the victory.
Auburn trailed by 11 points at halftime after Texas A&M made a 20-4 run after Auburn built a 17-11 lead with 12:54 left in the first half.
"We almost gave it away at the end," A&M coach Gary Blair said. "We were doing the little things right. Transition was our strength on offense. Our screens and our defense was pretty good. By far, that's the best team we've played all year. They (Auburn) are a very good ball club and well coached. Their point guard (Whitney Boddie) kept them in the ball game."
Auburn coach Nell Fortner said, "I thought we had a great effort by our team. We let them offensive rebound in the second half and get too many second chance opportunities. I felt that was really our biggest detriment to our team. We fought hard and had some really big plays at the end.
"Both teams came to play a really good basketball game and we just fell a little short," Fortner added. "This would have been a great win to beat another ranked team. We'll learn a lot from this game."
Each team had 37 rebounds and Auburn had 16 turnovers, one less than Texas A&M.
Auburn hit 22-57 field goals for 38.6 percent and was 4-10 on threes and 12-14 at the foul line. The Aggies made 26-60 field goals for 41.7 percent, 4-10 threes and 8-12 free throws.
AU's Greenleaf said, "In the first half we had too many turnovers. If we had limited our turnovers, it would have been a different ball game. It was a great atmosphere (at Reed Arena). The season isn't over for us and we will learn from it."
Sherell Hobbs scored 11 points and added five steals for Auburn while DeWanna Bonner added 10 points and five rebounds.