| Morton FC v Dumbarton 24/01/1959 | View match | |
| Montrose FC v Morton FC 31/01/1959 | View match | |
| Hamilton Academicals v Morton FC 07/02/1959 | View match | |
| Morton FC v Stenhousemuir FC 21/02/1959 | View match | |
| Morton FC v St Johnstone FC 07/03/1959 | View match | |
| Morton FC v Forfar Athletic FC 14/03/1959 | View match | |
| Albion Rovers FC v Morton FC 21/03/1959 | View match | |
| Morton FC v Ayr United FC 25/03/1959 | View match | |
| Cowdenbeath FC v Morton FC 28/03/1959 | View match | |
| Morton FC v Berwick Rangers FC 04/04/1959 | View match | |
| Arbroath FC v Morton FC 11/04/1959 | View match | |
| Dundee United FC v Morton FC 18/04/1959 | View match |