| 1. Round | 23/08/1958 | Bolton Wanderers | - | Leeds United | 4:0 | ||||
| 2. Round | 26/08/1958 | Leeds United | - | Luton Town | 1:1 | ||||
| 22. Round | 20/12/1958 | Leeds United | - | Bolton Wanderers | 3:4 | ||||
| 32. Round | 07/03/1959 | Aston Villa | - | Leeds United | 2:1 | ||||
| 33. Round | 14/03/1959 | Leeds United | - | Tottenham Hotspur | 3:1 | ||||
| 34. Round | 21/03/1959 | Manchester United | - | Leeds United | 4:0 | ||||
| 39. Round | 11/04/1959 | Leeds United | - | Blackburn Rovers | 2:1 | ||||
| 40. Round | 18/04/1959 | Newcastle United | - | Leeds United | 2:2 | ||||
| 41. Round | 22/04/1959 | Nottingham Forest | - | Leeds United | 0:3 | ||||
| 42. Round | 25/04/1959 | Leeds United | - | West Ham United | 1:0 |
Scotland