Following a 33-32 halftime deficit, UT began the second half with a 14-0 spurt, which led to a 46-33 lead with 13:32 left in the contest. From that point, the winners led until the end.
Damion James had 23 points and 11 rebounds, while Augustin added four rebounds and three assists for the top-seeded Longhorns (27-5), who have won 10 of their last 11 games.
Ibrahima Thomas led OSU with 19 points and five rebounds.
Obi Muonelo had 13 points, six rebounds and three assists and Terrel Harris added nine points for the Cowboys (17-15), who have lost three of their last four games and have a slight chance to get an NCAA Tournament bid when selections are announced on Sunday.