Texas led 49-46 with just under nine minutes left when Augustin took the game over, blowing past defenders for baskets or drawing fouls for free throws. He was 6-of-20 from the field but made up for it with an 11-of-12 effort from the line and timely layups when Texas needed them.
Oral Roberts looked like it might pull an upset equal to its win at then-No. 3 Kansas last season.
The Golden Eagles brought the most athletic lineup the Longhorns have faced on their home court this season, with 6-foot-10 center Shawn King causing problems in the middle early.
King scored eight points, the Golden Eagles outrebounded Texas 20-18 and had 11 second-chance points in the first half as the teams went into halftime tied 33-33. Texas missed a chance to take the lead when Damion James missed a two-handed putback dunk with about 15 seconds left.
A.J. Abrams, one of the Big 12's top 3-point shooters, was held scoreless in the first half on 0-for-4 shooting and took only one attempt from behind the arc.
Abrams finally caught on in the second half with two quick baskets that helped Texas build a 38-33 lead.
Oral Roberts' offensive rebounding disappeared in the second half. The Golden Eagles were held to one shot on four straight possessions and Augustin hit a 3-pointer that pushed the Texas lead to eight, the largest of the game to that point.
Texas couldn't put together the run to stretch its lead and it quickly shrunk to 49-46 when Marcus Lewis drove past two defenders for a tough layup and Kelvin Sango finished a fast break with an easy one.
Augustin took the game into his hands late to push Texas to the win.
His powerful drives drew fouls that sent him to the line for four straight points and another twisting, spinning burst through the lane left a defender tangled in his own feet as Augustin finished with a layup and a 60-49 lead with just over five minutes left.
Oral Roberts had plenty of time to catch up but the shots wouldn't go in. Augustin, meanwhile, kept bleeding seconds off the clock with his dribble.
The Golden Eagles had one last chance when a mistake by Augustin led to a turnover. Liberty hit a 3-pointer with 1:08 to play that cut the lead to 65-56 but Oral Roberts didn't score again.