| 1. Round | 14/09/1958 | Real Zaragoza | - | Real Sociedad | 1:0 | ||||
| 2. Round | 21/09/1958 | Granada CF | - | Real Zaragoza | 4:1 | ||||
| 3. Round | 28/09/1958 | Real Zaragoza | - | Sevilla FC | 4:2 | ||||
| 4. Round | 05/10/1958 | Athletic Club | - | Real Zaragoza | 3:2 | ||||
| 17. Round | 11/01/1959 | Real Zaragoza | - | Granada CF | 1:1 |
Spain