James Forrest's 17th club goal of the season put Celtic in front
Neil Lennon's Celtic continued their bid for a treble treble by sweeping aside nine-man Aberdeen to set up a Scottish Cup final against Hearts.
Dominic Ball was shown a second yellow after a sickening aerial challenge on Ryan Christie and Lewis Ferguson was shown a red for lunging at Tom Rogic. Boss Derek McInnes and assistant Tony Docherty were also sent to the stand.
James Forrest put Celtic ahead against the 10 men in first-half stoppage-time, Odsonne Edouard converted a penalty, and Rogic struck after Ferguson walked.
Celtic will meet Hearts at Hampden on 25 May - the first time they have met in a Scottish Cup final since 1956 - and the Scottish Premiership leaders need two more league wins to secure an eighth straight top-flight title.
The victory also moves Lennon a step closer to being given the manager's job on a permanent basis this summer.
'Aberdeen flattened by hooped juggernaut'
It wasn't just a Celtic landslide, it was an abject Aberdeen humiliation. Three goals conceded, two players sent off, a manager and an assistant manager sent to the stand - an utter collapse on the field and off in the face of opponents that were on it from the first whistle.
This was Celtic's 26th straight win in domestic cup competition, their 21st clean sheet, their 79th, 80th and 81st goals in this extraordinary run, while only seven have been given away at the other end.
They didn't just make the cup final, they strolled it in the kind of canter that brought a broad smile to Lennon's face and a haunted look on that of his counterpart McInnes as he sat in the stand alongside his assistant Docherty, the pair of them having been ordered off - Docherty during the break, McInnes 16 minutes before full-time.
The McInnes dismissal requires context. The Aberdeen manager was subjected to sectarian abuse from Celtic fans and he reacted to it, unwisely by his own admission. The twisted morality of these things in Scotland may now see McInnes up on a Scottish FA charge, while those guilty of abusing him will likely hear no more about it.
So many things had to go right for Aberdeen to halt this hooped juggernaut and the omens were grim even before a ball had been kicked when rumours of a Niall McGinn ankle injury in training on Saturday were confirmed. McGinn, in fine goalscoring form of late, missed this semi-final and will miss the rest of the season to boot.
Already shorn of suspended captain Graeme Shinnie and injured duo Gary Mackay-Steven and Shay Logan, the underdogs failed to muster even a yelp. The only bite they possessed was the kind that saw their discipline fall apart around their ears.
Jozo Simunovic, of all people, had two big chances to score inside the opening few minutes, Joe Lewis denying him the first time and, from the resulting corner, the centre-half side-footing wide when straight in front of the goal.
The Dons were under the cosh. They had a youthful team on the pitch and they were bossed from start to finish. The first of the reds came just after the half-hour when Ball, already booked for a silly trip on Jonny Hayes, arrived hopelessly late to an aerial duel with Christie and slammed his head into the midfielder's face. It was a horrible incident. Ball got a second yellow but the concern was all about Christie, who was tended to for six minutes before being taken away on a stretcher.
Rogic replaced Christie, Mikey Devlin came on for Stevie May and the Aberdeen horror show cranked up another notch.
Aberdeen's hopes all but evaporated after Dominic Ball was dismissedThree going on four, five, six
Cast the mind back to the last meeting of these sides at Hampden - the League Cup final earlier in the season - and a sickening head injury to Gary Mackay-Steven was followed in rapid order by a Celtic goal deep into first-half injury time. History repeated here, only this time it was Forrest who got that opener.
What a sumptuous goal it was, Forrest getting away from Max Lowe on the right before firing magnificently into Lewis's top right-hand corner. Brilliant and unstoppable. Forrest came close to making it two soon after.
Docherty got put to the stand during a half-time contretemps and Celtic piled on the heat from there. They had an urgency about them that Aberdeen struggled to live with when they had 11 men and two coaches. With 10 and one, they had no chance.
The second goal came when Devlin allowed a cross to drop over his head, a terrible piece of non-defending that had calamitous consequences when he brought down Hayes in an attempt to recover. Edouard tucked away from the penalty spot.
Aberdeen's heads had gone. Ferguson dived in recklessly on Rogic and got what he deserved - a straight red. From the free-kick, Celtic got what their dominance deserved - a third goal. Mikael Lustig's initial effort came off the defensive wall, but when the ball came back to him he laid it off to Rogic, who planted a precise shot beyond Lewis.
Three could have been four, five or six. In the midst of all this, McInnes was ordered off - a fourth departure on a most dismal day.
Celtic's victory was as emphatic as any of the 25 that preceded it. It has also bolstered Lennon's case for getting the job on a permanent basis. The treble treble is very much on. Only Hearts can stop them now.
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