The Volunteers were co champions of the Southeastern Conference with Auburn and Alabama (who gave the Vols their only loss) after a 5-6 campaign the previous year.
Nine minutes into the second quarter, Carl Pickens intercepted a Quinn Grovey pass while the Razorbacks were in Vols territory, returning it to the 13.
Arkansas had three more drives in the quarter, but only managed seven points out of them, turning the ball over on downs on one, and missing a field goal on the other.
The Razorbacks scored with 1:25 remaining on a Billy Winston pass from Grovey to narrow it to 31-27 after the missed conversion.
Arkansas tried to get the ball back on the onside kick, but Alvin Harper of the Vols recovered, as they ran out the clock and won their first Cotton Bowl Classic since 1951.