Jamie Murphy scored the only goal as Ayr United beat Partick Thistle 1-0 at Firhill in the first leg of the William Hill Premiership play-off quarter-final.
The second leg takes place at Somerset Park on Friday, live on BBC Scotland, with the winners up against Livingston in the semi-final next week.
Airdrieonians defeated Stenhousemuir 3-1 at Ochilview in the first leg of the Championship play-off semi-final while Queen of the South and Cove Rangers drew 0-0 at Palmerston.
Annan Athletic took a big step towards the William Hill League 1 play-off final by beating Elgin City 4-2 at Borough Briggs while Edinburgh City defeated East Fife 1-0 at Meadowbank.
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