That dream wasn’t to last, however, as the German giants, already 2-0 up from a first leg game played at Easter Road in Edinburgh two weeks previously, went on to score another two after half-time to win 4-1 on aggregate and go on to win the cup.
It was good while it lasted, though, and fans of the Kirkcaldy side will always have their memories of those precious moments when the unlikeliest of cup upsets briefly seemed possible.
Here are some photos of the first-leg tie, by SNS Group and Getty Images, as a reminder of those magic moments ...
1. Raith Rovers v Bayern Munich
No 9 Jurgen Klinsman knocks the ball into the Raith Rovers net to score for Bayern Munich in October 1995's UEFA Cup second round game at Easter Road in Edinburgh. Photo: SNS Group Photo: SNS Group
2. Raith Rovers v Bayern Munich
Raith Rovers' defence struggles to scramble the ball clear from danger during October 1995's UEFA Cup second round game at Easter Road in Edinburgh against Bayern Munich. Photo: SNS Group Photo: SNS Group
3. Raith Rovers v Bayern Munich
Bayern Munich's Jurgen Klinsmann, right, wins the ball ahead of Raith Rovers' Shaun Dennis in October 1995's UEFA Cup Winners' Cup second round game at Easter Road in Edinburgh. Photo: SNS Group Photo: SNS Group
4. Raith Rovers v Bayern Munich
Raith Rovers' Jim McInally, left, battles for the ball with Bayern Munich's Dietmar Hamann in October 1995's UEFA Cup second round game at Easter Road in Edinburgh. Photo: SNS Group Photo: SNS Group