A grandstand second half display from the Dons was not quite enough to rescue the game.
There were three changes for the Dons from the side beaten at Livingston on Saturday, with Scott Brown, Declan Gallagher and Dylan McGeouch all returning to the line-up in place of Adam Montgomery, Funso Ojo and Teddy Jenks, the latter two on the bench, Montgomery unavailable against his parent club.
Following their 4-0 win at Motherwell on Sunday, taking their unbeaten run to 19 games, Celtic made two changes for the trip to Pittodrie, Jota and Matt O'Riley in the starting XI in place of Tom Rogic and Georgios Giakoumakis, who both drop to the bench.
The game opened quietly, the sides feeling each other out, Aberdeen settling into their system of three at the back. Vicente Besuijen got in behind the Hoops' defence on seven minutes, but his cutback took an unfortunate deflection and was cleared to safety.
Celtic had the first real opening on 14 minutes, Rakston collecting the ball on the overlap and crossing for Maeda. He was up above the defence but from a central position, he glanced his header wide of goal.
Celtic were in front on 16. O'Riley bent in a teasing cross from their right and as Gary Woods and Calvin Ramsay hesitated, Jota darted in between them at the back post to stab the ball in.
After a decent start, a very disappointing goal to lose.
It was 2-0 four minutes later, though there was a huge element of misfortune in it after Celtic had slicked the ball around nicely. O'Riley picked up the ball from Gallagher's header clear on the edge of the box, but his shot was going nowhere when it hit David Bates' heel and flashed into the bottom corner with Woods wrongfooted. A massive deflection.
The Dons steadied themselves thereafter and while Celtic had the bulk of possession, it was without creating any further threat until the 36th minute when Maeda accelerated beyond the defence and drive a low cross through the box, Jonny Hayes tidying things up at the back post with Abada lurking. Aberdeen were finding it impossible to string anything together in an attacking sense though, and that remained the case to the break.
HALF-TIME: ABERDEEN 0 CELTIC 2
There were two changes for the home side at the break, Funso Ojo and Matty Kennedy replacing Ramsay and McGeouch, the Dons reverting to a back four with Hayes and Ross McCrorie at full-back. David Bates was in the book on 49 minutes for a mistimed challenge on Abada.
There was a much better opening to the half from the Dons and a period of prolonged possession in Celtic's third gave McCrorie the chance to get on the overlap. He fizzed a cross through the six yard box, Christian Ramirez just short of getting his head on it as he threw himself at the ball on 53 minutes.
A lovely free-kick got Aberdeen back into the gameon 56. Out on the left, rather than hoist in a cross, Ojo rolled a low ball in towards the penalty spot. Ramirez peeled away, nobody went with him and from ten yards out, he drilled it through a crowd of players and into the bottom corner.
Ramirez thought he had squared things up two minutes later, a lovely finish from Brown's header forward, but the assistant's flag - rightly - had gone up for offside.
Celtic were feeling the pace now and Jota was in the book for hacking McCrorie down on the hour as he looked set to get a cross in. Full revenge was exacted though for from the free-kick, Ojo curled the ball into the near post, Lewis Ferguson getting in front of everyone and glancing his header beyond Hart and in - 2-2.
Parity lasted less than a minute. Celtic were away back up to the Red Shed, for the first time in the half. A header ballooned forward, Jota turning away from Hayes and Bates before hammering a shot into the ground that bounced up and over Woods and in. Abada blocked off Bates as the ball came in, having looked marginally offside in the lead up to the goal, the assistant keeping his flag down.
From the kick-off, Gallagher was booked for hauling down Maeda as Celtic won the ball back. On 67 minutes there were raucous appeals for an Aberdeen penalty as Ferguson looked to have been barged to the ground, but again, nothing doing from the officials.
Aberdeen were causing havoc in the Celtic defence with crosses and it was the same again after 69 minutes, Hayes standing one up to the back post, Ferguson up to it, forcing Hart into an acrobatic save.
With 16 minutes left, Besuijen did well to win a flick on from Ramirez and then win a free-kick just right of centre, 25 yards out. Ferguson dug out a vicious drive that bent round the wall but went just over - Hart wasn't getting that one had it been a foot lower.
Celtic were forced into a couple of changes to try to change the tide, Maeda and Hatate making way for Giakoumakis and Bitton after 76 minutes. They did the same to run the clock down with Rogic and Forrest on for O'Riley and Abada on 89 minutes.
As we headed into four minutes of added time, Ramirez exchanged oases with Ferguson on the edge of the box, his attempt to bend the ball into the far corner going wide, and with it, the final hope of rescuing a point.