Scottish League Cup holders Celtic will meet Ross County in the semi-final of this season's tournament.
The draw at Hampden also paired Hibernian, currently second in the Championship, with St Johnstone.
The games will be played on the weekend of 30 and 31 January, with the venues and kick-off times to be announced.
Celtic have won the tournament 15 times, Hibs are chasing a fourth victory, while Saints and Staggies are seeking a maiden success.
John Collins, assistant manager at Celtic, said he was "content" with the draw but warned that his players would have to "be on their toes".
"They will come and give it everything as they always do," he said of County.
"They are playing very well, great team spirit, and we'll have to play very well."
County lost 4-1 at home to Celtic on Sunday as the champions maintained their six-point lead at the top of the Premiership.
The Dingwall side have beaten Celtic twice in the 15 previous meetings between the clubs, including a Scottish Cup semi-final success at Hampden in 2010.
Staggies goalkeeper Scott Fox, who is recovering from injury, said of the draw: "It's a tough one, the one people would try to avoid, but it's our job to beat them now.
"You have to beat the best teams to win a cup. I'm looking forward to it."
Hibs dropped out of the top flight in 2014, the same year St Johnstone won the Scottish Cup for the first time.
The Edinburgh side last lifted the League Cup in 2007, beating Saints after extra time to get to the final.
Alan Stubbs' team are on an unbeaten run of 13 games, winning 12 of those, while the Perth outfit, fourth in the Premiership, have won seven of their past eight matches.
BBC Scotland will provide live radio coverage of both ties and screen one live on television and online.