27th May 1995
| Final | Celtic | 1-0 |
11th April 1995
| Semi Final Replay | Celtic | 3-1 | Hibernian |
8th April 1995
| Semi Final | 1-0 | Heart of Midlothian |
7th April 1995
| Semi Final | Hibernian | 0-0 | Celtic |
12th March 1995
| 5th Round | Heart of Midlothian | 2-1 | Dundee United |
11th March 1995
| 5th Round | 1-4 |
| 5th Round | 0-4 | Hibernian |
10th March 1995
| 5th Round | Celtic | 1-0 | Kilmarnock |
20th February 1995
| 4th Round | Heart of Midlothian | 4-2 | Rangers |
18th February 1995
| 4th Round | Kilmarnock | 4-0 |
| 4th Round | 2-0 |
| 4th Round | Celtic | 3-0 | Livingston |
| 4th Round | 1-2 |
| 4th Round | Hibernian | 2-0 | Motherwell |
| 4th Round | 1-3 | Dundee United |
| 4th Round | 2-0 | Aberdeen |
7th February 1995
| 3rd Round Replay | 3-3 | Livingston |
| 3rd Round Replay | 1-5 | Dundee United |
| 3rd Round Replay | Heart of Midlothian | 2-1 |
| 3rd Round Replay | 4-0 |
6th February 1995
| 3rd Round | 0-2 | Motherwell |
| 3rd Round | 1-3 | Rangers |
| 3rd Round | Livingston | 1-1 |
1st February 1995
| 3rd Round | 1-1 | Heart of Midlothian |
| 3rd Round | 1-0 |
| 3rd Round | 1-2 |
31st January 1995
| 3rd Round Replay | 1-2 | Kilmarnock |
| 3rd Round | 1-1 |
29th January 1995
| 3rd Round | 2-1 |
28th January 1995
| 3rd Round | Aberdeen | 1-0 |
| 3rd Round | Celtic | 2-0 | St. Mirren |
| 3rd Round | 0-4 |
| 3rd Round | Dundee United | 0-0 |
| 3rd Round | 7-0 |
| 3rd Round | Kilmarnock | 0-0 |
| 3rd Round | 0-2 | Hibernian |
| 3rd Round | 1-0 |
17th January 1995
| 2nd Round Replay | 2-1 |
14th January 1995
| 2nd Round Replay | 3-1 |
| 2nd Round Replay | 5-2 |
9th January 1995
| 2nd Round | 2-2 |
7th January 1995
| 2nd Round | 2-3 |
| 2nd Round | 1-4 |
| 2nd Round | 6-2 |
| 2nd Round | 2-1 |
| 2nd Round | 0-1 | Livingston |
| 2nd Round | 2-6 |
| 2nd Round | 2-2 |
| 2nd Round | 2-3 |
| 2nd Round | 4-0 |
| 2nd Round | 0-0 |
| 2nd Round | 0-2 |
26th December 1994
| 1st Round | 2-5 |
19th December 1994
| 1st Round Replay | 3-0 |
17th December 1994
| 1st Round | 3-0 |
| 1st Round | 1-2 |
| 1st Round | 3-3 |