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Former Aberdeen loanee Ryan Christie scored the only goal as Brendan Rodgers led Celtic to his seventh straight domestic trophy and the club's 18th Scottish League Cup.
Dons winger Gary Mackay-Steven was knocked out by a clash of heads and carried off before Christie's strike in first-half injury time.
Celtic won a controversial 52nd-minute penalty but Scott Sinclair's spot kick was brilliantly saved by Joe Lewis.
Aberdeen could not find a leveller.
And Celtic could have doubled their lead when Sinclair broke free in the box but floated over, Lewis twice denied Odsonne Edouard, and the French striker spurned a great opportunity to play in a team-mate on an injury-time counter-attack.
The victory was Celtic's 22nd successive cup win since Rodgers took charge in the summer of 2016.
Ryan Christie fired past Joe Lewis at the second time of asking to put Celtic ahead
The final had been tighter than a drum before Christie's clinical moment, a game of huge intensity where Aberdeen went virtually man-for-man on Celtic's most influential midfielders and managed to all-but stifle their danger.
They had a scary moment early on when Tom Rogic saw a shot slap back off Lewis' right-hand post, but in the main it was an even contest.
Dominic Ball, Graeme Shinnie and Lewis Ferguson were in the faces of Christie, Callum McGregor and Rogic. Out wide, Sinclair wasn't getting any change out of Shay Logan down the left and James Forrest was in a battle with Max Lowe down the right.
Dons boss Derek McInnes would have been a happy man with the way things were going until late in the opening half. Their problems, ironically, started when they created a decent chance. Logan swung in a cross which was met by Mackay-Steven who headed straight at Bain.
What happened in the process of Mackay-Steven heading the ball was awful and deeply worrying. A clash of heads between the Aberdeen winger and Dedryck Boyata halted play for six or seven minutes. Boyata got up and a bandage was applied to his bloody wound. Mackay-Steven didn't get up, however. There was significant concern about his wellbeing as he lay on the floor.
Eventually, he was stretchered away and the final carried on into the final minutes of the half. That's when Aberdeen suffered their second blow, a double-whammy of disappointment. Five added minutes of six had been played when Boyata floated a ball over the top and into Aberdeen's penalty area.
Christie came to life in the blink of an eye, getting away from Shinnie and into space left by Aberdeen's sleeping centre-halves. The midfielder was one-on-one with Lewis, but the goalkeeper blocked his first attempt. When the ball fell loose, Christie was again the most alert man in Hampden. Even though he was falling over at the time he managed to stay in the moment, fend off Logan, and put the rebound into the Aberdeen net.
Joe Lewis dived to his right to deny Scott Sinclair from 12 yards
Celtic - now bearing down on seven titles in a row under Rodgers - turned up the heat in the new half. Poor officiating gave them a golden chance to make it 2-0 when Ball was adjudged to have handled in the box. He didn't. When ball struck arm, the arm was outside the penalty area, but referee Andrew Dallas gave Celtic the decision and Sinclair stepped up.
Lewis' save was magnificent, the goalkeeper flinging himself to his right and beating the ball away. Moments later he went the other way to deny Filip Benkovic. The Dons were reeling.
Just after the hour, Boyata came off and was replaced by Jozo Simunovic who was on the field a matter of seconds when he stuck out a leg in trying to dispossess Niall McGinn and only managed to poke the ball on to his own crossbar. That was a dramatic moment - and it wasn't the last of them.
Things opened up and tempers became frayed. Scott Brown came on to the field and Celtic pushed for a second. McGregor launched a counter-attack and played in Sinclair whose dinked effort fell wide.
All the while, Aberdeen fought and scrapped to get themselves back into it. They threw their heart and soul into everything. James Wilson appeared off the bench and his hooked effort was saved by Bain. How the Dons craved a gilt-edged chance in those closing moments, but Celtic were too organised, too confident, too good.
They should have scored a second minutes from the end when Odsonne Edouard broke free and went himself when a simple pass to Sinclair or Kieran Tierney would have given Celtic a near-unmissable opportunity. Profligacy didn't cost them, though. They saw it out and won the day - again.
