[3] Ranked fourth to start the year, the #2 Longhorns defeated rival Oklahoma by ten points on October 11,[4] and gained the top spot in the polls in late November.

On December 6, #1 Texas traveled to Fayetteville to meet second-ranked Arkansas;[5][6] down by fourteen points in the fourth quarter, UT rallied to win 15–14 in the season's "Game of the Century," attended by President Richard Nixon.

Longhorn QB James Street then led his squad to its first touchdown, and as coach Darrell Royal had planned, Texas attempted and completed the two-point conversion, which would in all likelihood prevent a tie.

Arkansas then had the ball and the lead, and a 73-yard drive later, the Hogs were in good position to tack on a field goal that would put the game out of reach, but Razorback QB Bill Montgomery was intercepted in the end zone, giving the Longhorns new life.

The extra-point snap was high, but was snared by third-string QB Donnie Wigginton and the kick was converted by Longhorn kicker Happy Feller, giving Texas a 15–14 lead with 3:58 to play.