Cove Rangers saw off the Rangers B team 5-1 at the Balmoral Stadium thanks to goals from Fraser Fyvie (2), Mitch Megginson, Jamie Masson and Leighton McIntosh.
Raith Rovers beat Inverness CT 5-4 on penalties after it finished 0-0 in the Highland capital.
Jack Sanders struck twice in the closing minutes as Kilmarnock edged out Hamilton Accies 3-2 in a dramatic match at New Douglas Park.
Queen of the South host Morton on Wednesday, live on BBC ALBA at 7.30pm.
Kilmarnock v Raith Rovers
Cove Rangers v Queen of the South or Morton
Semi-finals – midweek of March 1/2
Final – weekend of April 2/3