It was the first Aggie lead since holding a 5-4 lead four minutes into the game.
The Aggies and Huskers were tied 18-all with 8:12 left in the first half before Nebraska went on a 19-6 run to take 37-24 halftime lead.
Nebraska extended their lead to 18 points in the second half, a margin they held as late as the 14:02 mark, 48-30.
For the next twelve minutes the Aggies chipped away at the Husker lead, outscoring Nebraska 17-6, but Nebraska still held a 7-point lead 54-47 with 1:42 left in the game.
Nebraska's Cookie Miller missed a pair of free throws with 19.5 seconds left and the teams each turned the ball over twice before Texas A&M got a final possession.
A Nebraska foul gave the Texas A&M the ball out of bounds with 2.6 seconds left, still trailing 55-54.
Josh Carter received the inbounds pass and swished a 3-pointer from the top of the key as time ran out.
The Aggies scored 10 of the game's final 11 points.
Nebraska (16-10, 6-7) scored just seven points in the final 14 minutes and made just two field goals in the last 16:52.
Carter led Texas A&M with 11 points and Bryan Davis had 10 for the Aggies. Ade Dagunduro led Nebraska with 16 points.
Texas A&M (20-8, 6-7 Big 12) wins its third game in a row to keeps its hopes alive of receiving an NCAA tourney invite.