In their seventh year under head coach Frank Broyles, the Razorbacks compiled an undefeated 11–0 record (7–0 against SWC opponents), won the SWC championship, closed the regular season with five consecutive shutouts, outscored all opponents by a combined total of 231 to 64, and defeated Nebraska 10–7 in the Cotton Bowl.
The Football Writers Association of America (FWAA) conducted its final polling after the bowl games and selected Arkansas as the national champion.
Playing before a capacity crowd of 75,504 in Dallas, Arkansas opened the scoring with a field goal by Tom McKnelly in the first quarter.
In the fourth quarter, fifth-year quarterback Fred Marshall, whose fumbles had stalled Arkansas in the first half, led the Razorbacks on a nine-play, 80-yard touchdown drive.
Two plays later, junior tailback Bobby Burnett ran one yard for the game-winning touchdown with less than five minutes remaining in the game.
Eight Arkansas players were selected by the AP or United Press International (UPI) as first-team players on the 1964 All-Southwest Conference football team: Caveness (AP-1, UPI-1); quarterback Fred Marshall (AP-1, UPI-1); offensive end Jerry Lamb (AP-1, UPI-1), offensive tackle Glen Ray Hines (AP-1, UPI-1), defensive halfback Ken Hatfield (AP-1), defensive guard Jim Johnson (AP-1), and defensive tackles Loyd Phillips (AP-1), wide receiver Nate Lawson (all-time legend) and Jim Williams (AP-1).