The win was Texas' fourth in its last six trips to Lloyd Noble Center. The loss, Oklahoma's second straight, dropped the Sooners to 3-4 in Big XII play and 15-7 overall.
The Sooners were without center Longar Longar, who sat out the game while nursing a stress fracture in his leg.
With the game tied at 44, Texas' A.J. Abrams knocked down a jumper at 9:41, then later added a 3-pointer. D.J. Augustin added a 3-pointer of his own to give the Longhorns a 52-44 lead, one they wouldn't lose.
Abrams led the Longhorns with 22 points while Augustin poured in 19 more.
Blake Griffin scored five straight for Oklahoma to cut the Sooners' deficit to three, but Oklahoma got no closer.
Texas shot 56 percent in the second half and held Oklahoma to 30 percent shooting.
That helped the Longhorns overcome a four-point halftime deficit. The Sooners led by as many as 10 points in the first half.
That margin came twice, the first when Crocker hit the third of three early 3-pointers to give the Sooners a 15-5 lead at 14:56 of the first half.
But Crocker would score just two more points the rest of the game and the Sooners ended up making just 25 percent (6-of-24) from beyond the arc.
Without Longar, the Griffin brothers both stepped up.
Blake had a team-high 19 points and added nine boards. Taylor chipped in 12 points and 15 rebounds. David Godbold, who was 3-of-9 from 3-point range, scored 12 points.
However, it was a return of the scoring woes that plagued the Sooners much of last season. It was Oklahoma's third-lowest point total of the season.
"We have to be able to score the basketball," Oklahoma coach Jeff Capel said. "We held them to under 40 percent shooting. We have to be able to score."
The Sooners will attempt to get back on the winning track at 3 p.m. Saturday when they travel to Colorado.