The Aggie defense held Clemson All-Ameercian candidate Trevor Booker to just 6 points in the first half and 18 points for the game.
Clemson (4-1) lost for the first time this season.
Texas A&M had a 33-20 halftime lead and led by as many as 17 early in the second half before Clemson pulled to 58-56 when Tanner Smith made two free throws with 5:14 remaining. Smith finished with 14 points.
A free throw and a Holmes' 3-pointer gave the Aggies some breathing room and that was as close as Clemson would come.
The Aggies started the game stone cold, not scoring a basktet for the first six and a half minutes of the game. But the Aggies kept their composure and a consistently fierce Aggie defense kept the A&M deficit within reach, 7-1, until the offense caught fire.
Texas A&M tied the game at 7-7 on a David Loubeau layup at the 12:26 mark in the first half.
The game stayed close for the next few minutes and was tied 18-18 at with six minutes left in the first half.
Clemson's 20 points in the first half were the fewest the Tigers have scored since getting only 17 against Florida State on Feb. 19, 2008.
Texas A&M extended its advantage to 44-29 before Clemson used a 13-4 run to get back into the game.
The Aggie defense held Clemson to just 34% shooting and forced 19 turnovers.
Looking ahead, this was a very important win for the Aggies, as Clemson is one of its strongest non-conference opponents this season, and the win will help the Aggies' post season seeding if they continue to progress.
Friday's game with No. 8 West Virgina is another opportunity for the Aggies to get some positive national exposure and recognition.