The Scottish FA Cup was played for the 75th time in 1959/60 . The most important football cup competition in Scottish club football was directed and hosted by the Scottish Football Association. He started on 30 January 1960 and ended with the final on 23 April 1960 at Hampden Park of Glasgow . FC St. Mirren started as defending champions in the competition, which won against FC Aberdeen in the final last year . In this year's Scottish Cup final, the Glasgow Rangers and FC Kilmarnock faced each other. For the Rangers it was the 23rd final since 1894 . The Killies reached the finals for the seventh time since 1898 . The Rangers won the final 2-0. It was the first cup win since 1953 and the 15th overall for the Glasgow club. The FC Kilmarnock lost after 1932 , 1898 and 1957 , the fourth final result. In the 1959/60 season , the Rangers were third in the table, Kilmarnock runner-up. Scottish champion and league cup winner was Heart of Midlothian . As cup winners, the Rangers took part in the European Cup Winners' Cup the following season , and lost the final against Fiorentina from Italy.