The Aggies earned a shot against top-seeded Kansas by avenging a three-point home loss to the Sooners during the regular season.
The other first-round game Wednesday saw Oklahoma State run over Texas Tech 76-60, moving the Cowboys into the quarterfinals for a matchup with Missouri.
Baylor will play Kansas State and Iowa State will take on Texas in the other quarterfinal games Thursday.
Texas A&M improved to 14-17, pulling away down the stretch despite making only 18-of-46 from the field. Romero Osby scored 17 points for Oklahoma, which finished its season at 15-16.
Oklahoma State put together a 20-9 run early in the second half after Texas Tech had moved in front by a point.
The Cowboys (15-17) shot 51 percent from the field and made all 16 of their foul shots. Keiton Page led the way with 20 points and Brian Williams had 19.
Jordan Tolbert scored 16 for the Red Raiders (8-23).