| 2. Round | 14/10/1978 | AFC Ajax | - | EVV Eindhoven | 3:2 | ||||
| Round of 16 | 18/11/1978 | AFC Ajax | - | Roda JC Kerkrade | 3:0 | ||||
| Quarter-finals | 20/03/1979 | Fortuna SC | - | AFC Ajax | 0:2 | ||||
| Quarter-finals | 04/04/1979 | AFC Ajax | - | Fortuna SC | 2:0 | ||||
| Semi-finals | 18/04/1979 | FC Volendam | - | AFC Ajax | 3:3 | ||||
| Semi-finals | 24/04/1979 | AFC Ajax | - | FC Volendam | 1:1 | ||||
| Final | 15/05/1979 | AFC Ajax | - | FC Twente '65 | 1:1 | ||||
| Replay finale | 29/05/1979 | AFC Ajax | - | FC Twente '65 | 3:0 |  |
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