| 1. Round | 14/09/1958 | UD Las Palmas | - | Real Madrid | 1:2 |  |
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| 2. Round | 21/09/1958 | Real Oviedo | - | UD Las Palmas | 2:1 | ||||
| 3. Round | 28/09/1958 | UD Las Palmas | - | Sporting Gijón | 4:0 | ||||
| 10. Round | 16/11/1958 | UD Las Palmas | - | Sevilla FC | 3:0 | ||||
| 11. Round | 23/11/1958 | UD Las Palmas | - | Real Zaragoza | 3:1 |
Argentina