Ross County’s reward for knocking out Betfred Cup holders Celtic is a quarter-final trip to managerless Livingston.
Stuart Kettlewell’s side stunned Celtic 2-0 at Parkhead to hand under-pressure Neil Lennon and his side their first domestic cup defeat in 36 games.
Steven Gerrard’s Rangers will now be the favourites to lift the Ibrox club’s first major trophy since 2011 after hammering Falkirk 4-0.
But the Light Blues will have to survive a trip to Paisley to face St Mirren if they are to book a Hampden slot for the semi-finals.
Gers keeper Jon McLaughlin said: “Great – it’s another away tie which we will have to give full respect and full attention to once it comes round.
“Of course we’ll feel that’s another winnable game again but we won’t look beyond it. We’ll prepare for it once it comes around and fingers crossed we can do another professional job like we did today.”
The other last-eight clashes see Championship side Alloa hosting Jack Ross’ Hibernian, while Dunfermline will welcome St Johnstone to East End Park.
The ties will take place across three nights between December 15-17.