Following their 3-1 win at Falkirk on Tuesday night, Ally McCoist’s side were first out of the hat when the draw was made at Tannadice following Dundee United’s last-gasp 1-0 win over neighbours Dundee.
The Ibrox side were paired with St Johnstone, who also played on Tuesday, beating Kilmarnock 1-0 at Rugby Park.
United’s reward for their derby win, thanks to a 90th-minute Jaroslaw Fojut header against ten men, was a trip to face Alan Stubbs’ Hibernian, who defeated Ross County 2-0 in the Highlands on Tuesday.
The most dramatic of last night’s ties was at New Douglas Park where Hamilton beat local rivals Motherwell 6-5 on penalties after the game finished scoreless after extra time, with both sides reduced to ten men.
Celtic will host Partick Thistle in the quarter-finals afer the Jags saw off St Mirren 1-0 on Tuesday.
After the draw Celtic manager Ronny Deila said: “I never said I wanted to draw Rangers in the next round. I only said that the game is coming.
“I’m pleased to have another home draw against Thistle. We want to win this competition so we will look forward to that game.”
On-loan Manchester City striker John Guidetti opened the scoring for Celtic before a Kris Commons penalty and Adam Eckersley own goal sealed the win and Deila added: “I was happy that Guidetti got his first goal. He has been out for a long time and not played that many matches and that’s why we don’t use him for 90 minutes. He made a huge impact tonight and that was good.
“We gave away some chances but they were down to individual mistakes and they are things that we can work on. We had plenty of opportunities to score and I felt we were well worth our win.”
Rangers striker Kris Boyd believes his team are now ready to take on Premiership opposition, but accepted that they will need to improve on their current form if they are to progress to the last four. Before beating Falkirk, Rangers did defeat top-flight opposition in the shape of Inverness Caledonian Thistle in the previous round.
Boyd said: “The majority of the teams left are Premiership teams, so we have an opportunity to show how far we have come. The performance against Falkirk wasn’t great in terms of getting the ball down and passing, and we struggled there earlier in the season, but we ran out comfortable winners.
“We are in a position where we can cause teams from the Premiership problems and we showed that against Inverness.
“They’re second in the league and have beat Celtic and played reasonably well, so we know we can cause problems. However, the way we have played this season, there are three or four teams from the Premiership that we would have to raise our game against to beat them.”
Scottish League Cup quarter-finals:
Rangers v St Johnstone
Hibernian v Dundee United
Aberdeen v Hamilton
Celtic v Partick Thistle
Ties to be played on Tuesday 28 and Wednesday 29 October.