Match ends, Celtic 5, Partick Thistle 0.
Holders Celtic eased past Partick Thistle to win their 29th successive domestic cup tie and set up a Scottish League Cup semi-final with Hibernian.
Vakoun Issouf Bayo headed in his first Celtic goal to open the scoring before Tom Rogic finished a flowing move.
Second-tier Thistle, in their first game under new boss Ian McCall, had Tam O'Ware's header ruled out for offside.
And Olivier Ntcham's seven-minute double, then Scott Sinclair's strike, sealed Celtic's last-four berth.
Celtic have won the competition three years running as one third of their domestic treble treble.
Thistle, bottom of the second tier, harried Neil Lennon's men will in the first half, but faded after the interval.
Five-star Celtic show strength in depth
If Celtic thought they'd have everything their own way against the team propping up the division below, they had another thing coming, certainly in the first half. Under McCall, returning this week for his second stint as manager, Partick were energised and organised, hard-working and disciplined.
They didn't buckle after Jonny Hayes' cross was perfectly weighted for Bayo to head home. And that speaks volumes about the improvement from Saturday's insipid 3-0 loss to Dunfermline Athletic.
The avalanche of goals from the much-changed champions simply didn't materialise. Some of those given a chance to shine failed to advance their cause for more regular action. Mohamed Elyounoussi and Lewis Morgan struggled to influence the game from out wide and were outshone by full-backs Hayes and Jeremie Frimpong, an impressive debutant.
Bayo came close from another Hayes cross, but it was the burgeoning Thistle who carved out the next big chance. Celtic gave the ball away and only a fine Craig Gordon save denied Shea Gordon as he galloped into the area.
Would Lennon's side heed that warning? The answer came within 40 seconds of the restart. Rogic applied the perfect finish to a fine Celtic move, with the hosts immediately showing the increased urgency their manager had presumably just demanded.
Then came the show-stopper. Ntcham's thunderous blast from at least 30 yards settled any lingering nerves. The Frenchman added a sumptuous second after robbing Raffaele de Vita on the left and curling in off the inside of the far post.
Sinclair applied the cherry to the cake after Thistle meekly surrendered the ball to Bayo, and where Rogic couldn't finish, the substitute could on just his fifth outing of the campaign.
An emphatic victory for a Celtic team showing eight changes from Saturday's win over Kilmarnock.
Man of the match - Olivier Ntcham
Ntcham delivered two fine goals, and was the main man in the middle of the park during a rampant second-half display.
All good things came through him, and when you consider the explosive power of his first goal, and the technical quality of his second, almost passed into the side netting, it would be harsh not to give the award to the Frenchman.
'A professional performance' - reaction
Celtic manager Neil Lennon: "People on paper think those games are easy. It was a professional performance, some outstanding play, particularly in the second half. The main thing is we're in the semi-final, injury free."
Partick Thistle manager Ian McCall: "The scoreline was probably fair reflection of the game. We had a really good chance to make it 1-1. And at 2-0, it looks like we scored a perfectly good goal, but Celtic deserved to win.
"I was really, really pleased with the effort and togetherness and I think we can take them up the league."
- 30FrimpongBooked at 52minsSubstituted forHendryat 79'minutes
- 15HayesBooked at 54mins
- 42McGregorSubstituted forBrownat 62'minutes
- 27ElyounoussiSubstituted forSinclairat 66'minutes
- 3PenriceBooked at 81mins
- 7CardleSubstituted forDe Vitaat 59'minutes
- 14GordonSubstituted forColeat 74'minutes
- 9MillerSubstituted forMansellat 64'minutes
- 23De Vita
- Steven McLean
- Shots on Target
Second Half ends, Celtic 5, Partick Thistle 0.
Attempt missed. Lewis Morgan (Celtic) right footed shot from more than 35 yards is too high.
Attempt blocked. Vakoun Issouf Bayo (Celtic) left footed shot from outside the box is blocked.
Attempt missed. Olivier Ntcham (Celtic) right footed shot from outside the box misses to the right.
Attempt saved. Vakoun Issouf Bayo (Celtic) right footed shot from the right side of the box is saved in the bottom left corner.
Kristoffer Ajer (Celtic) wins a free kick in the attacking half.
Foul by Lewis Mansell (Partick Thistle).
Attempt missed. Olivier Ntcham (Celtic) right footed shot from outside the box is just a bit too high.
James Penrice (Partick Thistle) is shown the yellow card for a bad foul.
Lewis Morgan (Celtic) wins a free kick in the defensive half.
Foul by James Penrice (Partick Thistle).
Substitution, Celtic. Jack Hendry replaces Jeremie Frimpong.
Corner, Celtic. Conceded by Sean McGinty.
Goal! Celtic 5, Partick Thistle 0. Scott Sinclair (Celtic) right footed shot from very close range to the bottom right corner following a fast break.
Substitution, Partick Thistle. Reece Cole replaces Shea Gordon.
Corner, Celtic. Conceded by Scott Fox.
Attempt saved. Scott Sinclair (Celtic) right footed shot from the right side of the box is saved in the bottom left corner.
Attempt saved. Tomas Rogic (Celtic) left footed shot from outside the box is saved in the bottom right corner.
Substitution, Celtic. Scott Sinclair replaces Mohamed Elyounoussi.