TCU tied for second in the Southwestern Conference, in the penultimate season for Coach Abe Martin, and first bowl game since 1959.
TCU dominated the first half with 48 rushing plays to Texas Western's 20, which led to a 10–0 halftime lead.
In the fourth quarter, the Miners scored early on an 18-yard field goal, to take the lead at 13–10 after recovering a fumble at the 29.
TCU scored with 43 seconds left after sacking Stevens in the end zone, to make it 13–12.
[1] The Miners would return to the Sun Bowl two years later and win (by then, Texas Western had become UTEP).