I do know we beat #1 Ole Miss on the road in 1964. Cats had a pretty good team that year (QB Rick Norton, RB Roger Bird, etc.). Mississippi had the pre-season #1 ranking, but it was probably undeserved as their season wasn't a success.
No. 1 Ole Miss (Sept. 26, 1964)
Kentucky earned an early upset of the nation’s No. 1-ranked team in the second week of the 1964 season. With a 27-21 win in Jackson, Mississippi, Kentucky knocked the Rebels’ season off the rails. Despite opening the season at No. 1, Ole Miss finished it at 5-5-1 with a loss to Rice in the Bluebonnet Bowl.
Kentucky’s upset of No. 6 Ole Miss marked just the fifth time the Wildcats have beaten a top-six team in program history.
ca.sports.yahoo.com