The Longhorns will play either Kansas or Texas A&M in the title game on Sunday afternoon.
Oklahoma scored the first seven points of the second half to tie the game at 36-36, but the Sooners' momentum quickly stopped and never got restarted.
After Cade Davis tied the game with a 3-pointer at 17:59, the Sooners missed their next six shots and went scoreless for 4:32.
Abrams added another 3-pointer as Texas used a 12-2 run to push its lead to 19 points, one that continued to grow throughout the half.
The Sooners (22-11) got 20 points and 13 rebounds from freshman forward Blake Griffin.
Tony Crocker, with 11 points, was the only other Sooner in double figures. Oklahoma managed just 20 second-half points and was 4-of-23 (.174) from 3-point range.
Austin Johnson didn't score for the Sooners, but did dish out a career-high 10 assists.
Now it's the waiting game for the Sooners, who find out Sunday night their NCAA Tournament destination and opponent.