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Celtic were too strong for a spirited Raith Rovers side as they cruised into the Scottish Cup quarter-finals.
Liam Scales' stunning strike gave Ange Postecoglou's men a first-half lead.
But the well-drilled Championship team were well in the game before the hosts lifted themselves out of their slumber with Giorgos Giakoumakis and Daizen Maeda scoring in quick succession.
Nir Bitton added gloss to the scoreline when he netted a late fourth on the rebound from his saved penalty.
There was further good news for Celtic with Christopher Jullien making his comeback after a 13-month injury lay-off.
Postecoglou's side will find out their opponents in the last eight on Monday following the tie between Peterhead and Dundee.
In their last three games Celtic had been adept at taking the game to their opponents early on with eight of their 10 goals being scored before half-time.
And they set their stall out early against John McGlynn's visitors with Mikey Johnston and Bitton shooting over and Rea Hatate drilling a shot into the hands of goalkeeper Jamie MacDonald.
Scales broke Raith's resistance when he opened up his left foot and cracked a shot in off the post that MacDonald could not get close to.
Celtic were fortunate not to concede a penalty when a bouncing ball appeared to hit the arm of defender Cameron Carter-Vickers inside the box, but Raith's appeals were dismissed by referee Steven McLean.
There were other nervous moments in Celtic's box as Raith committed men forward, but the visitors struggled to get a meaningful shot on target and goalkeeper Joe Hart was a virtual spectator.
Giakoumakis hit the crossbar but it is unlikely it would have counted with Johnston offside when he played the ball across.
Celtic had hit a lull before Jota's introduction gave them a lift, the winger creating a chance for Tom Rogic before he was instrumental in Giakoumakis making it 2-0.
The Greek striker timed his run to beat the offside trap and knocked in Jota's inch-perfect pass.
Soon it was three when Maeda got to a corner. MacDonald made a great save initially, but could only knock it off the Celtic man and back over the line.
A controversial penalty made it four when Sean Mackie was harshly penalised for handball. Bitton bundled it home after his first effort was saved by MacDonald, with the 4-0 scoreline a touch harsh on Raith.
Man of the match - Liam Scales
What did they say?
Celtic manager Ange Postecoglou: "We weren't great in the first half. We didn't work hard enough, we didn't play at a tempo, took too many touches of the ball. The second half was better.
"We made seven changes to the team so you know it's not going to be as fluent or as cohesive. It's not about singling out individuals. We have an intent and ambition to be a certain kind of team, training is intense so game day we are intense no matter who starts, and I think the urgency wasn't quite there."
Raith Rovers manager John McGlynn: "I thought we were very well organised and disciplined in our play. We knew Celtic would come out the traps and bombard us early on and we wanted to get beyond that period, which I thought we did.
"There was a claim for a penalty, but I haven't seen it back. I am proud of the players and we have to get our league campaign going again."
Player of the match
JotaJota
with an average of 7.84
Celtic
Squad number17Player nameJota
Squad number20Player nameCarter-Vickers
Squad number41Player nameHatate
Squad number5Player nameScales
Squad number18Player nameRogic
Squad number7Player nameGiakoumakis
Squad number38Player nameMaeda
Squad number56Player nameRalston
Squad number15Player nameHart
Squad number11Player nameAbada
Squad number57Player nameWelsh
Squad number2Player nameJullien
Squad number6Player nameBitton
Squad number21Player nameIdeguchi
Squad number49Player nameForrest
Squad number19Player nameJohnston
Raith Rovers
Squad number1Player nameMacDonald
Squad number2Player nameTumilty
Squad number4Player nameMusonda
Squad number16Player nameStanton
Squad number8Player nameMatthews
Squad number6Player nameBenedictus
Squad number3Player nameDick
Squad number20Player nameWilliamson
Squad number9Player nameGullan
Squad number7Player nameConnolly
Squad number22Player nameRoss
Squad number11Player nameZanatta
Squad number18Player nameVarian
Squad number99Player namePoplatnik
Squad number25Player nameArnott
Squad number21Player nameMackie
Line-ups
Celtic
Formation 4-3-3
- 15Hart
- 56Ralston
- 20Carter-VickersSubstituted forJullienat 74'minutes
- 57Welsh
- 5Scales
- 18RogicSubstituted forIdeguchiat 69'minutes
- 6Bitton
- 41Hatate
- 49ForrestSubstituted forAbadaat 69'minutes
- 7GiakoumakisSubstituted forMaedaat 69'minutes
- 19JohnstonSubstituted forNeves Filipeat 55'minutes
Substitutes
- 1Barkas
- 2Jullien
- 3Taylor
- 11Abada
- 16McCarthy
- 17Neves Filipe
- 21Ideguchi
- 29Bain
- 38Maeda
- 42McGregor
- 84Doak
Raith Rovers
Formation 4-2-3-1
- 1MacDonald
- 2Tumilty
- 4Musonda
- 6BenedictusSubstituted forMackieat 80'minutesBooked at 83mins
- 3Dick
- 20WilliamsonSubstituted forZanattaat 45'minutes
- 16Stanton
- 7ConnollySubstituted forVarianat 64'minutes
- 8MatthewsBooked at 87mins
- 22RossSubstituted forArnottat 85'minutes
- 9GullanSubstituted forPoplatnikat 64'minutes
Substitutes
- 11Zanatta
- 17Thomson
- 18Varian
- 21Mackie
- 25Arnott
- 26Mitchell
- 29Young
- 99Poplatnik
Live Text
Match ends, Celtic 4, Raith Rovers 0.
Second Half ends, Celtic 4, Raith Rovers 0.
Offside, Celtic. Reo Hatate tries a through ball, but Liel Abada is caught offside.
Foul by Christopher Jullien (Celtic).
Matej Poplatnik (Raith Rovers) wins a free kick on the left wing.
Goal! Celtic 4, Raith Rovers 0. Nir Bitton (Celtic) right footed shot from the centre of the box to the centre of the goal following a set piece situation.
Penalty saved! Nir Bitton (Celtic) fails to capitalise on this great opportunity, right footed shot saved in the bottom right corner.
Ross Matthews (Raith Rovers) is shown the yellow card for hand ball.
Attempt blocked. Jota (Celtic) right footed shot from the left side of the box is blocked.
Penalty conceded by Sean Mackie (Raith Rovers) with a hand ball in the penalty area.
Nir Bitton (Celtic) wins a free kick in the attacking half.
Foul by Ross Matthews (Raith Rovers).
Substitution, Raith Rovers. Aaron Arnott replaces Ethan Ross.
Sean Mackie (Raith Rovers) is shown the yellow card for a bad foul.
Daizen Maeda (Celtic) wins a free kick on the left wing.
Foul by Sean Mackie (Raith Rovers).
Foul by Daizen Maeda (Celtic).
Dario Zanatta (Raith Rovers) wins a free kick in the defensive half.
Substitution, Raith Rovers. Sean Mackie replaces Kyle Benedictus because of an injury.
Substitution, Celtic. Christopher Jullien replaces Cameron Carter-Vickers.