Celtic will face Rangers in the Scottish Cup semi-finals after seeing off a battling Dundee United.
A deflected shot from Callum McGregor gave the visitors a half-time lead, while a dreadful blunder from goalkeeper Ben Siegrist resulted in a tap-in for Giorgos Giakoumakis.
The striker grabbed a late second goal, helping on an effort from substitute Karamoko Dembele.
United pressed valiantly but posed little threat in attack at Tannadice.
The win stretches the Scottish Premiership leaders’ run of unbeaten domestic games to 30.
Celtic, who have lifted the cup a record 40 times, join Rangers, Hearts and Hibernian in the last four – the first time the Glasgow and Edinburgh clubs have all made it this far together.
And, with the League Cup already in the trophy room and a three-point lead in the league, fans’ thoughts will be turning to a potential fifth treble in six seasons.
Follow radio & text coverageAmid the early hustle and bustle, Celtic forward Daizen Maeda brushed the roof of the net from a long way out.
The breakthrough came on 12 minutes when McGregor ran on to a short corner and let fly from the edge of the penalty area. Nicky Clark stuck a leg out in an attempt to block, but only succeeded in diverting the ball away from Siegrist.
The goal knocked the stuffing out of the home side for a while, as did the loss of energetic midfielder Ian Harkes to injury, but a wild challenge from Reo Hatate on Kieran Freeman reignited United after half an hour.
However, an increase in aggression and work-rate did not stem the flow of Celtic attacks and there was a moment of controversy when the visitors thought they had scored a second goal.
Maeda squeezed a shot in from close range but the ball had come his way via the arm of Giakoumakis. It wasn’t a deliberate action from the Greek, with the changed rulebook therefore suggesting the goal should have stood.
Soon after, McGregor sent a fizzing effort just wide of the top corner and a swivelling Giakoumakis then volleyed off target.
The hosts continued to graft commendably after the interval, although they were undone by too many errant passes.
Just when it looked like Celtic had been knocked off their stride, they were handed a gift by Siegrist, who fumbled a cross from Maeda at the feet of Giakoumakis and the striker could not miss.
Thereafter, Ange Postecoglou’s side managed to keep United at bay without too much fuss and found a late goal when Dembele’s deflected shot looped up nicely for Giakoumakis to nudge home.
Man of the match – Callum McGregorCeltic captain Callum McGregor knocked in the opener and helped his midfield overcome determined opponents with a typically assured displayWhat the managers saidDundee United’s Thomas Courts: “We stuck to the task but probably just didn’t work the goalkeeper enough and we didn’t give our fans – who I thought were tremendous throughout – anything to really shout about and make a real game of it.”
Celtic’s Ange Postecoglou: “We didn’t really give them any opportunities to get near our goal. We scored three goals away from home and I thought we handled the atmosphere well. Away from home, a 3-0 win in a knock-out game is pretty comprehensive.”
Player of the match
McGregorCallum McGregor
with an average of 7.24
Dundee UnitedSquad number2Player nameSmith
Squad number1Player nameSiegrist
Squad number18Player nameButcher
Squad number12Player nameEdwards
Squad number29Player nameGraham
Squad number22Player nameFreeman
Squad number19Player nameLevitt
Squad number7Player nameNiskanen
Squad number10Player nameClark
Squad number23Player nameHarkes
Squad number9Player nameMcNulty
Squad number46Player nameThomson
Squad number17Player nameMeekison
Squad number3Player nameSpörle
Squad number6Player nameMcDonald
CelticSquad number42Player nameMcGregor
Squad number7Player nameGiakoumakis
Squad number20Player nameCarter-Vickers
Squad number88Player nameJuranovic
Squad number49Player nameForrest
Squad number33Player nameO’Riley
Squad number38Player nameMaeda
Squad number3Player nameTaylor
Squad number15Player nameHart
Squad number41Player nameHatate
Squad number77Player nameDembele
Squad number4Player nameStarfelt
Squad number18Player nameRogic
Squad number16Player nameMcCarthy
Squad number19Player nameJohnston
Squad number21Player nameIdeguchi
Line-upsDundee UtdFormation 3-5-2
1Siegrist
18Butcher12Edwards29Graham
22Freeman2Smith19Levitt23Harkes7Niskanen
10Clark9McNulty
1Siegrist18ButcherBooked at 49mins12Edwards29Graham22FreemanSubstituted forSpörleat 66’minutes2Smith19LevittSubstituted forMeekisonat 72’minutes23HarkesSubstituted forMcDonaldat 28’minutes7NiskanenBooked at 57mins10Clark9McNultySubstituted forThomsonat 71’minutesSubstitutes3Spörle4Mulgrew6McDonald13Eriksson15Akinola17Meekison46Thomson58Anim CudjoeCelticFormation 4-3-3
15Hart
88Juranovic20Carter-Vickers4Starfelt3Taylor
33O’Riley42McGregor41Hatate
49Forrest7Giakoumakis38Maeda
15Hart88Juranovic20Carter-Vickers4Starfelt3Taylor33O’RileySubstituted forMcCarthyat 76’minutes42McGregorSubstituted forIdeguchiat 87’minutes41HatateBooked at 30minsSubstituted forRogicat 45’minutes49ForrestSubstituted forJohnstonat 76’minutes7GiakoumakisBooked at 86mins38MaedaSubstituted forDembeleat 76’minutesSubstitutes2Jullien6Bitton10Ajeti16McCarthy18Rogic19Johnston21Ideguchi29Bain56Ralston57Welsh77DembeleReferee:John Beaton
Attendance:8,553
Live TextMatch ends, Dundee United 0, Celtic 3.
Second Half ends, Dundee United 0, Celtic 3.
Greg Taylor (Celtic) wins a free kick on the left wing.
Foul by Miller Thomson (Dundee United).
Corner, Dundee United. Conceded by Josip Juranovic.
Goal! Dundee United 0, Celtic 3. Giorgos Giakoumakis (Celtic) right footed shot from the centre of the box to the bottom left corner.
Attempt blocked. Karamoko Dembele (Celtic) left footed shot from the right side of the box is blocked. Assisted by Tomas Rogic with a through ball.
Substitution, Celtic. Yosuke Ideguchi replaces Callum McGregor.
Karamoko Dembele (Celtic) wins a free kick in the defensive half.
Foul by Miller Thomson (Dundee United).
Giorgos Giakoumakis (Celtic) is shown the yellow card for a bad foul.
Foul by Giorgos Giakoumakis (Celtic).
Archie Meekison (Dundee United) wins a free kick in the defensive half.
Corner, Celtic. Conceded by Ross Graham.
Attempt blocked. Liam Smith (Dundee United) right footed shot from outside the box is blocked. Assisted by Archie Meekison.
Foul by Michael Johnston (Celtic).
Archie Meekison (Dundee United) wins a free kick in the defensive half.
Tomas Rogic (Celtic) wins a free kick on the right wing.
Foul by Adrián Spörle (Dundee United).
Substitution, Celtic. James McCarthy replaces Matt O’Riley.