Colorado raced to a 13-2 lead in the first five and a half minutes of play.
The Aggies committed 19 turnovers, most of them in the first half, as Colorado built a 32-24 halftime lead.
Texas A&M outscored Colorado 16-5 the first seven minutes of the second half to take a 40-37 lead.
Colorado fought back to take a 54-49 lead with 5:55 left in the game
A&M regained the lead, 58-56, on a Donald Sloan layup and extended the lead to ficve, 61-56, with three minutes remaining.
With this win, the Texas A&M (22-8, 8-7 Big 12) took a big step towards an NCAA tourney invite.
Colorado pulled back to within two, 68-66, with 17 seconds left, before B.J. Holmes and Derrick Roland each sunk pairs of free throws to ice the win.
Texas A&M hosts No. 12 Missouri on Saturday. A win over Missouri would likely make the Aggies a lock to get their NCAA tourney invite.