Ole Miss finished 4th in the Southeastern Conference for the second straight year in a row.
The Longhorns finished 3rd in the Southwest Conference, attending a bowl game after a two season wait.
Bill Bradley started the scoring on his 25 yard touchdown run to give them a 6-0 lead.
Ole Miss tried to narrow the lead with a Jimmy Keyes field goal from 43 yards out.
Bradley ran for his second touchdown of the day to make it 19-0, as Texas coasted from there to win.