Texas A&M struggled much of the first half as Baylor opened up a twelve-point lead, 24-12, when Anthony Jones hit a 3-pointer with 7:32 to go in the first half.
The Aggies fought back to pull to within one, 33-32, with 47 seconds left in the first half, before Quincy Acy sunk two free throws to give the Bears a 35-32 halftime lead.
It was a back and forth game in the second half, with the lead changing hands five times.
Texas A&M scored the first four points of the second half to take a brief lead, 36-35, before Baylor regained the lead, 47-41, at the 13:54 mark in the second half.
The Aggies took a 48-47 lead on a David Loubeau free throw with 11:39 on the clock.
Tweety Carter's 3-point jumper with just under ten minutes left in the game gave the Bears a seven-point lead, 55-48.
B.J. Holmes made 3-pointers with 5:19 and 4:52 remaining to bring the Aggies within one point each time.
Texas A&M again came back to take the lead, 65-64, when Bryan Davis hit two free throws with 3:21 to go.
From there, the Aggies made 12 of 14 free throws down the stretch and Holmes came through again from long range with 1:31 remaining, when his 3-pointer gave A&M a 72-66 lead, as Texas A&M cruised to a huge 78-71 Big 12 win over No. 20 Baylor.
Texas A&M survived another poor three-point shooting game, at one point just 1 of 13, finishing 4 of 18 (22%) after Holme's critical late 3-pointers.
This was in large part due to the Aggie rebounding advantage, 32-24, and an uncharacteristic 85% free throw shooting (28 of 33).
Bryan Davis scored 22 points, including hitting 8 of 9 free throws, and pulled down 8 rebounds to lead the Aggies.
The Aggies All-Big 12 candidate, Donald Sloan, scored 20, points. including 9 pf 10 free throws, and snagged 5 rebounds.
David Loubeau added 13 points and 5 rebounds.
LaceDarius Dunn led Baylor with 23 points.
Texas A&M (17-6) improved their Big 12 record to 6-3, tied for second behind Kansas.
The Aggies don't play again until next Saturday when they face Texas Tech in Lubbock.