Texas took a 56-43 lead on Connor Atchley's bucket and seemed ready to cruise home. But Terrel Harris made a 3-pointer and the Cowboys, ice cold from beyond the arc all day, then quickly drilled three more from long range during a 12-2 spree that cut the Longhorns' lead to 58-55.
James then sneaked inside for a layup and Justin Mason, following an Oklahoma State turnover, made it 62-55 with 2:17 left.
Top-seeded Texas, the regular-season co-champions with Kansas, will meet the winner of the Colorado-Oklahoma game in Saturday's semifinals. The Longhorns posted their fifth straight win over the Cowboys (17-15).
Ibrahima Thomas had 19 points for Oklahoma State, which trailed by as many as seven points in the first half before taking a 33-32 halftime lead on Harris' 3-pointer at the buzzer.
But all the momentum quickly deserted the Cowboys as Augustin took command after intermission. After hitting a 3-pointer on Texas' first possession, he coaxed a third foul against Oklahoma State point guard Byron Eaton and sank both free throws. Then a few seconds later he seized a Cowboys pass that was deflected to him by a teammate and dished to A.J. Abrams for a layup.
Abrams, scoreless the first half, connected again a moment later and then Augustin boosted the lead to 44-33 with his fifth 3-pointer.
The Cowboys, confused by a 2-3 zone they didn't see in the first half, missed 12 straight shots and went almost 8 minutes without a field goal until Obi Muonelo's 3-pointer. By then, the Longhorns had a 46-38 lead.
Freshman Gary Johnson, a part-time starter for the Longhorns, was helped off the court in the first half, not putting weight on his left foot, and did not return.
Muonelo had 13 points for Oklahoma State, which was only 9-of-31 from beyond the arc.
Much of the first half was a shooting contest between James and Thomas.
James, a 6-foot-7 sophomore, drilled his first five shots, including his first three 3-pointers. But Thomas, a 6-11 freshman, practically matched him shot for shot, making five of his first seven field-goal attempts and both his 3-pointers.
Atchley had seven rebounds and four blocks for the Longhorns.