Celtic manager Ange Postecoglou welcomed a home draw against Raith Rovers after his side beat Hearts 3-2 in the Premier Sports Cup.
The Hoops will host the Kirkcaldy side in the quarter-finals in a repeat of the 1994-95 final, which Raith won on penalties, after the Fifers knocked out Aberdeen.
Rangers will host Livingston while there will be two quarter-finals in Dundee. Holders St Johnstone will travel to the Kilmac Stadium at Dens Park while Dundee United will welcome Hibernian to Tannadice.
After winning a third home match in eight days, Postecoglou said to Celtic TV on the draw: "Another opportunity to play in front of our supporters here at Celtic Park and we are all looking forward to it.
"Every game in a cup competition is important so having home advantage is pleasing."
Odsonne Edouard and Stephen Welsh netted in a dominant first-half display from Celtic and Kyogo Furuhashi restored Celtic's two-goal cushion with his fifth goal of the season following Liam Boyce's penalty.
Hearts substitute Aaron McEneff gave the scoreline a flattering sheen deep in stoppage-time.
St Johnstone twice came from behind at Arbroath before winning 3-2 on penalties.
The Championship side lead through goals from Joel Nouble and Thomas O'Brien but Saints replied with goals from Glenn Middleton after 59 minutes and Jamie McCart just before half-time in extra time. Ali McCann netted the winning spot-kick.
Raith came from behind to beat Aberdeen 2-1. The Dons had led through Jay Emmanuel-Thomas' first goal for the club but the hosts grew as a force and second-half strikes from Ethon Varian and Dario Zanatta caused an upset for the Championship team.
Second-half goals from Kyle Magennis and Kevin Nisbet saw Hibernian bounce back from their midweek disappointment in Europe against Rijeka to defeat Kilmarnock 2-0.
The quarter-finals will take place on September 21-23.
