They were put under pressure by an Arthurlie team flying at the top of the West of Scotland League First Division. But Rose ended their two club records of 22 consecutive wins and 30 games undefeated.
Horn said: “It was a really tough game and it’s what we expected. They’re unbeaten all season and we’ve made changes as well to give boys game tie. Fair play to the boys, they showed plenty of heart and character.”
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Rose will face Dundonald Bluebell or Tranent in the quarter-finals. They can wrap up the Lowland League title with a win at Berwick Rangers on Saturday.