Dundee’s reward for their League Cup win over Falkirk will be a trip to face Europa League finalists Rangers at Ibrox.
The Dark Blues have been set the daunting task of taking on Giovanni van Bronckhorst’s Gers for a place in the semi-finals.
Dundee United, meanwhile, face a repeat of their opening league match of the season after they were paired with Kilmarnock.
Killie defeated Hearts at Tynecastle to tee up the all-Premiership quarter-final tie.
United responded to Tuesday’s sacking of Jack Ross with a long-awaited victory – their first domestic win of the season – on the road at Livingston.
Steven Fletcher opened the scoring early on before he set up Ian Harkes for the second goal in a 2-1 win at the Tony Macaroni Arena.
Last season, Tam Courts’ Tangerines made it to the final eight but were beaten by Ross’s Hibs 3-1 at Tannadice.
United have now reached the last eight of the League Cup in 12 of the last 16 seasons.
Gary Bowyer’s Dark Blues, meanwhile, booked their place in the last eight of the competition after a 3-0 victory over League One Falkirk on Tuesday.
Goals from Lyall Cameron, Lee Ashcroft and Zach Robinson sealed a fifth victory in five League Cup ties.
That’s after they grabbed a seeded spot in the group stages, seeing off Hamilton, Stranraer, Forfar and Queen’s Park.
It has been over 18 years since Dundee got beyond the quarter-finals, a Bobby Linn goal in 2003 defeating Hearts at Dens Park.
Draw in full
Kilmarnock v Dundee United
Rangers v Dundee
Aberdeen v Partick Thistle
Motherwell v Celtic
Games to be played over midweek October 18-20.
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