| 5. Round | 21/11/2020 | Arbroath FC | - | Greenock Morton FC | 0:0 |  |
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| 11. Round | 02/01/2021 | Alloa Athletic | - | Greenock Morton FC | 1:1 | ||||
| 13. Round | 15/01/2021 | Greenock Morton FC | - | Dunfermline Athletic | 0:0 | ||||
| 14. Round | 23/01/2021 | Queen Of The South | - | Greenock Morton FC | 2:1 | ||||
| 9. Round | 27/01/2021 | Greenock Morton FC | - | Inverness CT | 2:2 | ||||
| 15. Round | 06/02/2021 | Greenock Morton FC | - | Raith Rovers | 0:1 | ||||
| 17. Round | 20/02/2021 | Heart of Midlothian | - | Greenock Morton FC | 1:1 | |
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| 18. Round | 27/02/2021 | Greenock Morton FC | - | Dundee FC | 2:2 |  |
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| 19. Round | 06/03/2021 | Greenock Morton FC | - | Ayr United | 0:2 | ||||
| 16. Round | 09/03/2021 | Inverness CT | - | Greenock Morton FC | 0:1 | |
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| 20. Round | 13/03/2021 | Dunfermline Athletic | - | Greenock Morton FC | 1:0 | ||||
| 21. Round | 20/03/2021 | Greenock Morton FC | - | Queen Of The South | 2:1 | ||||
| 22. Round | 27/03/2021 | Raith Rovers | - | Greenock Morton FC | 1:0 | |
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| 23. Round | 06/04/2021 | Greenock Morton FC | - | Inverness CT | 1:4 | ||||
| 24. Round | 10/04/2021 | Dundee FC | - | Greenock Morton FC | 1:1 | ||||
| 27. Round | 30/04/2021 | Arbroath FC | - | Greenock Morton FC | 0:0 |
England