Leeds entered the competition in the third round and were drawn against Fourth Division team Southport. Jimmy Greenhoff opened the scoring for Leeds in the 26th minute at their home ground, Elland Road. Albert Johanneson added a second in the 81st minute and Terry Cooper scored a third before the end of the match to secure a 3–0 win for Leeds. Everton were the opposition in the fourth round. The match finished 1–1 at Elland Road, with Jim Storrie scoring Leeds' goal in the 50th minute. A replay was held at Everton's home ground, Goodison Park, three days later. Goals from Don Weston and Jack Charlton secured a 2–1 victory for Leeds and progression to the fifth round.
