Holders Celtic will take on either Hearts or St Mirren in the William Hill Scottish Cup semi-finals at Hampden Park next month.
Neil Lennon's team knocked out Rangers' conquerors Dundee United on Sunday, beating them 4-0 at Tannadice and Hearts and St Mirren, who drew 2-2 at Tynecastle on Saturday, face a replay for the right to face the Hoops.
Aberdeen, 2-1 winners at Motherwell on Sunday, will play Hibernian who beat Ayr 2-0 on Saturday.
Dons boss Craig Brown told Sky Sports: "We're delighted to be in the draw, all the teams are fairly even. Celtic are the best team (left in) I think and to avoid them is fortunate, but I'm not taking anything for granted.
"You see the way they played, we made heavy weather of the game today so we need to improve against Hibs in the semi-final."