Match ends, Rangers 5, Queen of the South 0.
Martyn Waghorn's second-half hat-trick helped Rangers cruise past Championship leaders Queen of the South into the Scottish League Cup semi-finals.
The hosts, winless in their last three games, only had Jason Holt's goal to show for a dominant first half.
But captain Andy Halliday clipped in the second and Waghorn shot from the edge of the box for his first.
The striker then converted Michael O'Halloran's cross before lashing home his eighth goal in seven games.
Rangers manager Mark Warburton appeared to be making a point when he appointed Halliday captain for the night, when Danny Wilson would normally have deputised for the absent Lee Wallace.
It was midfielder Halliday who was caught up in a training ground argument with Joey Barton, who has been suspended by the club for three weeks.
He played at the base of the midfield, kept play moving, allowing the players in front of him to press higher up the park because of his mobility, and generally led with a quiet assurance, even before he struck Rangers' second of the night with a composed finish from Barrie McKay's cross.
It seemed no coincidence that Rangers were also more effective with Jason Holt back in the side, with his darting runs beyond the forwards restoring a vital aspect that had been missing from the team's play this season.
Holt was alert and deft enough to finish off O'Halloran's delivery from close range for the opener.
Warburton made four changes to his starting line-up, and there are now issues for him to mull over as he prepares for Sunday's Premiership trip to Pittodrie. Lee Hodson was solid at full-back, but will surely be replaced by Wallace - who was rested - but others impressed.
O'Halloran created the first and fourth goals, crossing from the right for Waghorn to add his second from 10 yards out. The striker's first goal, eight minutes previously, was a crisp finish from inside the D.
O'Halloran's pace and direct running were a constant threat, and his presence on the flank allowed Waghorn to play as the central striker.
The latter was rewarded with a hat-trick, the third coming after Niko Kranjcar bundled the ball to him inside the area and he lashed it high into the net.
Harry Forrester worked hard and was composed - apart from a lunging foul on Jordan Matthews that might have brought more than a yellow card.
Warburton has yet to settled on his strongest XI, but he will welcome selection becoming more difficult due to individuals' improving form.
Queens subdued for once
The visitors are the top scorers in the Championship and their strike force of Derek Lyle and Stephen Dobbie have 17 goals between them in all competitions this season. They were restricted, though, to half-chances and endured a growing sense of frustration.
Queens were forced to play on the counter, which did not entirely suit two strikers who don't have the pace of old. The wide men - Grant Anderson and Dale Hilson - were working hard in defence, so support was scarce.
The visitors were more lively early in the second half, after Rangers dominated possession in the opening 45 minutes.
Both Lyle and Dobbie shot wide, and it was not to be their night.
Rangers manager Mark Warburton: "After what happened at Parkhead hard work is the only way of getting better.
"It was a pleasing night's work. We asked them to dominate the football in the first half and we did that completely.
"The only complaint from us as a group is that it was 1-0 at half-time and it could have been more.
"We scored goals but missed a lot of chances as well. The only difference from Saturday against Ross County was that we were a little bit more clinical and it helps build momentum."
Queen of the South manager Gavin Skelton: "I didn't think we played as well as we can in the first half.
"We started the second half not too bad actually but it's stating the obvious that goals do change games.
"We were on top for the first 10 minutes but then the second goal kills it."
- 6WilsonBooked at 11mins
- 23HoltSubstituted forMcKayat 45'minutes
- 29O'HalloranSubstituted forMillerat 77'minutes
- 15ForresterBooked at 59minsSubstituted forCrooksat 72'minutes
Queen of Sth
- 7AndersonSubstituted forDykesat 50'minutes
- 8MillarBooked at 44mins
- 14JacobsSubstituted forPickardat 68'minutes
- 9LyleSubstituted forBrotherstonat 69'minutes
- Don Robertson
- Shots on Target
Second Half ends, Rangers 5, Queen of the South 0.
Attempt missed. Stephen Dobbie (Queen of the South) right footed shot from outside the box misses to the left.
Attempt missed. Niko Kranjcar (Rangers) right footed shot from outside the box is close, but misses to the right.
James Tavernier (Rangers) wins a free kick in the attacking half.
Foul by Dale Hilson (Queen of the South).
Corner, Rangers. Conceded by Jamie Hamill.
Attempt saved. Stephen Dobbie (Queen of the South) right footed shot from outside the box is saved in the bottom right corner.
Goal! Rangers 5, Queen of the South 0. Martyn Waghorn (Rangers) left footed shot from the centre of the box to the top right corner. Assisted by Niko Kranjcar.
Attempt saved. Kenny Miller (Rangers) left footed shot from a difficult angle and long range on the right is saved in the bottom left corner.
Attempt missed. Dean Brotherston (Queen of the South) right footed shot from more than 35 yards is close, but misses to the left.
Corner, Rangers. Conceded by Jordan Marshall.
Niko Kranjcar (Rangers) wins a free kick in the defensive half.
Foul by Jake Pickard (Queen of the South).
Substitution, Rangers. Kenny Miller replaces Michael O'Halloran.
Hand ball by Lyndon Dykes (Queen of the South).
Attempt missed. James Tavernier (Rangers) right footed shot from the right side of the box is just a bit too high.
Attempt missed. Niko Kranjcar (Rangers) right footed shot from a difficult angle and long range on the right is close, but misses to the right.
Corner, Rangers. Conceded by Lyndon Dykes.
Substitution, Rangers. Matt Crooks replaces Harry Forrester.