First Division rivals Hamilton Academical and Dundee meet at New Douglas Park, while St Johnstone host Second Division Raith Rovers.
The only surviving Third Division outfit, Stenhousemuir, face a tough task away to First Division St Mirren.
Third round ties will take place on Tuesday 13 and Wednesday 14 September.
Bell's Cup third-round draw:
Stirling Albion v Morton
St Mirren v Stenhousemuir
Hamilton Academical v Dundee
St Johnstone v Raith Rovers
Ties will take place on 13/14 September
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