The Sooners set a school record for the fewest points allowed against a Big 12 opponent. The previous record of 41 had come against Colorado on March 7, 1997, and was matched against Baylor on March 6, 2004.
It was the third time in coach Jeff Capel's two seasons at Oklahoma that the Sooners have held an opponent below 40 points. Last season, the Sooners allowed 35 points in a win over Texas Christian and 36 in a win over Norfolk State.
Oklahoma is 26-4 all-time against Texas A&M, but had lost three in a row to the Aggies before Saturday.
Texas A&M (21-8, 7-7) had snapped a three-game losing streak with a 44-point rout of Texas Tech on Wednesday, the Aggies' largest margin of victory in a Big 12 game.
But the Aggies, who entered the game second in the Big 12 in field-goal percentage, made just 13 of 51 shots (25 percent) against Oklahoma, including 2 of 16 from 3-point range. The Aggies hadn't shot under 30 percent from the field in a game since shooting 26 percent against Texas on Feb. 16, 2005.
Josh Carter and DeAndre Jordan led the Aggies with 10 points each.
Oklahoma dominated the boards, posting a 42-28 rebounding advantage over a team that entered the game ranked fifth in NCAA Division I in rebounding margin.
Oklahoma's previous two wins, against Texas Tech and Baylor, came in the waning seconds on difficult shots, but the Sooners' defense ensured there would be no drama against the Aggies.
Texas A&M, unranked for the first time all season, led 10-9 after a dunk by Jordan with 12:50 left in the first half, but didn't score again before halftime. The Aggies made just 5 of 27 shots in the half.
Oklahoma had a 5-minute scoring drought of its own, but soon enough, the Sooners began pulling away, scoring the final 19 points of the half to take a 28-10 lead.
The second half didn't start much better for the Aggies, as a 3-pointer by Austin Johnson and a follow shot by Cade Davis pushed Oklahoma's margin to 33-10 with 18:21 left, resulting in a time-out by Texas A&M coach Mark Turgeon.
Bryan Davis' dunk with 16:42 left ended the Aggies' scoreless stretch, but Texas A&M never seriously threatened in the second half. Oklahoma built its lead to as many as 29 points.
Johnson and Blake Griffin each scored 13 points for Oklahoma. Griffin also had eight rebounds.
The Sooners shot 48 percent from the field, going 24 of 50.