It was a tight first half, as the lead changed hands five times.
Colorado opened up a 6-2 lead in the first two minutes of play before the Aggies went on 11-2 run to take a 13-8 lead at the 12:58 mark in the first half.
Colorado took a 26-25 lead with 3:52 to go in the first half and led at halftime 32-30.
Texas A&M opened the second half with a 15-6 run, taking a seven point lead, 45-38, on a David Loubeau layup with 12:25 left in the second half.
The Aggies extended their lead to nine, 49-40, on a Donald Sloan layup with 9:40 to go.
The Aggies still had a six point lead, 59-53, until Alec Burks made two free throws with 1:50 left in the game.
Colorado tied the game, 59-59, when Cory Higgins made two free throws with 53 seconds left.
On the ensuing possession, Donald Sloan missed a layup but Bryan Davis pulled down a rebound and dunked it to give A&M a 61-59 lead with 32 seconds left.
Alec Burks missed a jumper that would have tied the game with 21 seconds to go, Sloan rebounded and was fouled by Burks. Sloan made both free throws to extend the Aggie lead to 63-59 with 18 seconds on the clock.
Levi Knutson immediately fouled Donald Sloan but Sloan made both free throw attempts to give the Aggies a 65-61 lead with 6 seconds to go.
Cory Higgins made a layup with a couple of seconds left to cut the Aggie lead to 65-63.
B.J. Holmes was fouled and made both free throws to seal a 67-63 Big 12 win for the Aggies.
Texas A&M (14-5, 3-2) was fortunate to pull out a win despite hitting just 2-of-23 three-point attempts.
The win was Texas A&M's seventh straight over the Buffaloes and extended the Colorado's conference road losing streak to 32 games.
In addition to Sloan's 18 points for the Aggies, Nathan Walkup had 16 points and 8 rebounds while Bryan Davis added 12 points, 9 rebounds, and 3 blocked shots.
Cory Higgins and Alec Burks had 19 points each to lead Colorado (10-9, 1-4), which hasn't won a conference road game in more than four years.
Texas A&M travels to Stillwater to face Oklahoma State on Wednesday night.