Aberdeen beat Ross County 3-1 to move back into second place in the Scottish Premiership, profiting from Hearts' 2-2 draw at Motherwell.
Hearts failed to close the gap on Scottish Premiership leaders Celtic after drawing 1-1 with Dundee, as Dundee United lost again.
Celtic will play Ross County at Hampden in the League Cup semi-final, while St Johnstone face Hibernian in Edinburgh.
Hibernian will face St Johnstone and Ross County will play Celtic in the Scottish League Cup semi-finals in January.
Celtic put their European disappointment behind them as they won 4-1 at Ross County to stretch their Scottish Premiership lead.
Ronny Deila declared his disappointment in the Celtic fans who disrupted a minute's silence at Dingwall on Sunday.
Hearts moved above Aberdeen in to second place in the Scottish Premiership with victory over Partick at Firhill.
A review of Tuesday night's action in the Scottish League Cup as Ross County and St Johnstone progress to the semi-finals.
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