Morton won the shoot-out 3-1 after a 1-1 draw with Hibernian in Premier Sports Cup Group D.
In the other Group D fixture, Falkirk won 4-2 on penalties after a 1-1 draw at Bonnyrigg Rose so a draw against Clyde on Saturday will see the Bairns top the group.
In Group E, there was a 3-0 win for FC Edinburgh over Cowdenbeath at Meadowbank Stadium.
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