Augustin scored six straight points on Monday night as the Longhorns held OSU scoreless for a six-minute span for the second time in the game and took the lead, then hit all four of his free throws in the final minute to keep the Cowboys at bay.
OSU had a final chance to tie, but James Anderson's 3-pointer from the left side rimmed out with 11 seconds left.
Marcus Dove's putback attempt also missed, and Augustin corralled the rebound to earn another trip to the free throw line with 5.7 seconds left. He scored the final 10 points for Texas in its second straight two-point win.
Texas is 15-3 overall and 2-1 in Big 12 Conference play while OSU falls to 10-8 and 1-3. The loss was OSU's first in 10 home games this season.
Anderson led OSU with 17 points.