Holders Celtic face a trip to Tynecastle to play Hearts in the Scottish League Cup quarter-finals following Monday's draw at Hampden.
Inverness Caledonian Thistle host a Highland derby against Ross County in the second all-Premiership tie.
Championship side Hibernian, who knocked out Premiership leaders Aberdeen, host Dundee United, with Greenock Morton home to St Johnstone.
The ties will be played on 27 and 28 October.
Celtic knocked out Hearts 3-0 on their way to winning last season's tournament.
But Robbie Neilson's side held the Scottish champions to a 0-0 draw in Glasgow on league duty on Saturday to end an 10-game losing streak against Celtic.
Celtic first-team coach John Kennedy said: "I think they are an improved side and Robbie's got them playing well.
"They showed a side to them that they maybe haven't all season - defensively they were very well organised and there was a real willingness to defend their goal.
"It is a tough draw - probably as tough as we could have got and it'll be an exciting game when it comes around."
Hearts striker Gavin Reilly thinks the Edinburgh side can go one better.
"It is a home draw, it will be a sell-out at Tynecastle and all the fans will be looking forward to it," he said.
"We went to Parkhead on Saturday and got a good away point, so we're home for this tie and hopefully we can beat them in the Cup."
Hibs and United also met in last season's tournament, with the Tannadice outfit extending their winning run in fixtures between the side to five games.
However, the Edinburgh side will believe they have a chance of going one better than losing 7-6 on penalties after a 3-3 draw with the Tangerines struggling in second-bottom place in the top flight.
Morton get another chance to cause an upset against a Premiership side as they host the Saints after knocking out Motherwell in the previous round.
The last meeting between Morton and St Johnstone was also in the League Cup, with the Perth side winning 1-0 at Cappielow to extend their unbeaten run against the Greenock outfit to 11 games.
Morton's last win over Saints came in the League Cup in September 2006 at Cappielow.
Caley Thistle and County meet for the first time this season on Saturday in the Premiership.
Inverness are unbeaten in their last five meetings with County, but the Victoria Park outfit drew on their last two visits to Caledonian Stadium and won 3-1 in the one before that.
County midfielder Rocco Quinn told BBC Scotland: "We would have probably liked a home tie, but to get Caley at their bit is as near a home tie as we are going to get.
"We're pleased with the draw and we're looking forward to the game.
"We're very happy with the way we're playing right now. It's obviously early days yet, but I think we've got a very strong squad and we're really looking to progress in the Cup this year.
"Caley were fantastic last season. They had a bit of a slow start this season, but they are beginning to come into their own."
Quinn does not think it is beyond County to win the trophy for the first time.
"With the squad, the management and the chairman we have at the club, it's definitely realistic for us and we as a club and a team want to achieve something," he said.
"So lifting this Cup would be immense for us."
Caley Thistle defender Gary Warren was looking forward to facing County.
"It is a good draw for us in terms of travelling and it is a local derby," he said.
"We've got them this Saturday, so that will give a little indication for where we are and where Ross County are and it should bode well for an interesting quarter-final."
Scottish League Cup quarter-final draw
Hibernian v Dundee United
Greenock Morton v St Johnstone
Inverness Caledonian Thistle v Ross County
Hearts v Celtic
Ties on 27 and 28 October