Despite trailing to an early second-half goal from the home side's Jamie Winter, Celtic always had the better possession and control of the game. Their three-goal burst in ten minutes was a fair reflection of their supremacy.
Aberdeen were dealt a serious blow prior to kick-off when skipper Russell Anderson cried off with a migraine. In a re-shuffled back four, Winter was called in alongside Alexander Diamond in the centre of the Dons defence.
Celtic boss Gordon Strachan made three changes to the side which lost surprisingly at home last Saturday to lowly Dunfermline. Chris Sutton was injured whilst Mo Camara and Alan Thompson dropped out of the side altogether. The trio were replaced by Ross Wallace, Shunsuke Nakamura and Maciej Zurawski.
Celtic passed up an excellent chance on four minutes when a throughball from Nakamura carved open the inexperienced Dons rearguard. Stilian Petrov latched onto the ball, but from a good position he failed to pick out the unmarked John Hartson at the far post.
A moment of indecision by Andrew Considine saw him caught in possession by Zurawski on 15 minutes, but the striker's attempted lob flew harmlessly over the crossbar.
Aberdeen's first real effort on goal came on 25 minutes when a Jamie Smith free-kick from 28 yards dipped just the wrong side of the upright.
Minutes later Celtic passed up another great opportunity when Diamond's back header was never going to reach Ryan Esson. Zurawski was onto the ball swiftly but he was too casual with his effort allowing the Dons keeper the smother his effort at the expense of a corner.
Celts keeper Artur Boruc had to look lively immediately after the re-start. A Barry Nicholson free-kick picked out the run of Diamond whose header across the area was nicked off the head of Stevie Crawford by the Pole.
It was game on in the 52nd minute when a short free-kick from Nicholson found Winter whose first-time effort flew into the bottom of the net to give the home side an unlikely lead.
Celtic's response was immediate. The Dons defence failed to clear a Zurawski cross and the ball ricocheted around the box before falling to Aiden McGeady who lashed the ball home from 14 yards giving Esson no chance.
Disaster struck for the home side on 58 minutes when Esson failed to hold a Hartson snap-shot and the ball fell kindly to Petrov who easily rolled his shot home.
Celtic went further ahead on 65 minutes with a very simple goal. A short Nakamura corner was dummied by McGeady into the path of Paul Telfer who then waltzed past Nicholson before blasting home a low shot past the unsighted Esson.
Trickery by Shaun Maloney left several Dons defenders in his wake on 86 minutes, but with the goal at his mercy the diminutive striker's weak effort was easily held by Esson.
As the game entered stoppage time Esson was very fortunate to stay on the park. Substitute Adam Virgo burst between Aberdeen centre-backs Considine and Diamond and attempted to lift the ball over the advancing Dons keeper who handled the ball outside the area.
Much to the surprise of everyone in the ground, referee Charlie Richmond only produced a yellow card.