Rangers, who struggled for long periods in their 2-1 win over Falkirk yesterday, were drawn with St Johnstone who had beaten Motherwell on Saturday.
Tonight Celtic are at Morton, the winners meeting either Ayr United or Dundee United, who meet in the fourth quarter-final on Saturday.
Darren Dods and Miguel Simao were the heroes for St Johnstone in their win at Fir Park, while the Rangers coach, Dick Advocaat, expressed disappointment with his team's display against Falkirk, of the First Division.
Neil McCann and Lorenzo Amoruso were on target but after David Moss had equalised McCann's goal, Stefan Klos, the Rangers goalkeeper, had to rescue his side on several occasions.
"There were some very poor performances," Advocaat said. "Falkirk did well. They were well organised at the back and looked fresher than us today".
The semi-final against St Johnstone has again paired the League Cup finalists of earlier in the season, with Rangers winning 2-1 on that occasion.
But Sandy Clark, the St Johnstone manager, commented: "We have played Rangers a few times this season and have been getting closer to them, so hopefully this time we can go one better."
Celtic travel to Greenock to take on a Morton side managed by one of their former employees. Billy Stark was assistant to Tommy Burns for three years at Celtic: he has spent much of this week playing down talk of revenge, but will be determined that his side puts up a good show in what will be the last big occasion to be held at their antiquated Cappielow Ground.
Dundee United overcame the challenge of First Division Clydebank after a replay, and as Paul Sturrock's side has struggled in the tournament they can anticipate a tough tie at Ayr, where Kilmarnock were beaten in an earlier round.
Ian Wallace has pleaded with Dumbarton to tell him why he has been suspended as manager. Wallace was told by the club chairman Douglas Dalgleish after the 2-0 defeat by East Stirling yesterday to stay away from the Scottish Third Division club while an inquiry is carried out.
n Jim Farry has protested his innocence in the Jorge Cadete affair that led to his suspension as Scottish Football Association chief executive. He faces judgement at Hampden Park today when the SFA Council discuss his future.Reuse content