Falkirk booked their place in the last four of the Scottish Cup by beating Queen of the South 1-0 at Palmerston on Friday night.
Craig Sibbald's first-half header was the difference between the teams, who are separated only by goal difference in the Championship.
Peter Houston's men can now look forward to the semi-finals on the weekend of April 18, meaning their league game at home to Cowdenbeath will require to be rearranged.
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