| Date | Location | Result | |
| Dec 4, 1976 | Austin, Texas | Texas 29, Arkansas 12 | Box score |
| Nov 25, 1976 | Austin, Texas | Texas A&M 27, Texas 3 | Box score |
| Nov 20, 1976 | Waco, Texas | Baylor 20, Texas 10 | Box score |
| Nov 13, 1976 | Fort Worth, Texas | Texas 34, TCU 7 | Box score |
| Nov 6, 1976 | Austin, Texas | Houston 30, Texas 0 | Box score |
| Oct 30, 1976 | Lubbock, Texas | Texas Tech 31, Texas 28 | Box score |
| Oct 23, 1976 | Austin, Texas | Texas 13, SMU 12 | Box score |
| Oct 9, 1976 | Dallas, Texas | Texas 6, Oklahoma 6 | Box score |
| Oct 2, 1976 | Houston, Texas | Texas 42, Rice 15 | Box score |
| Sep 18, 1976 | Austin, Texas | Texas 17, North Texas State 14 | Box score |
| Sep 11, 1976 | Chestnut Hill, MA | Boston College 14, Texas 13 | Box score |