Hoops keeper Craig Gordon was the busier keeper in the first-half before an initial mistake from his Dons counterpart Scott Brown led to defender Jason Denayer heading the home side into a 37th minute lead from a corner.
The visitors, so impressive before the break, fell apart in the second-half and after several close calls striker Leigh Griffiths made it 2-0 with a penalty in the 63rd minute before midfielders Gary Mackay-
Steven and Stefan Johansen added further goals.
It was Celtic’s third win over the Granite City club this season to end second-placed Aberdeen’s 13-game unbeaten league run with the visitors looking a sorry lot by full-time.
Ronny Deila’s side also have a game in hand over the Pittodrie side, at home to St Johnstone on Wednesday night.
The Hoops boss made three changes for the keenly-awaited lunch-time encounter. Griffiths recovered from an ankle knock to take over from the benched John Guidetti, defender Efe Ambrose replaced Emilio Izaguirre who injured his hand in the Europa League defeat by Inter Milan in the San Siro on Thursday night and midfielder Kris Commons came in for Stuart Armstrong, who took his place among the substitutes.
Midfielder Jonny Hayes made a surprise recovery from a hamstring complaint to replace Peter Pawlett who started on the bench.
The home side started a little nervy but in the fourth minute it was Griffiths who flashed a low drive just wide of the target from the edge of the box, setting the game alight.
Moments later, Gordon brilliantly tipped a curling shot from former Celt Niall McGinn over the bar for a corner.
When Hayes fired the ball over midfielder Kenny McLean drove it towards goal with defender Andrew Considine re-directing his header over the bar.
The home side suffered a blow in the 11th minute when Commons, just back from a hamstring complaint, was replaced by Armstrong before a penetrating Hayes run ended with him slewing shot across goal and wide
An absorbing match continued just after the half-hour mark, as Aberdeen swarmed around the Hoops’ box again, Gordon made a save from Pittodrie midfielder Ryan Jack, before Hayes hobbled off to be replaced by Pawlett.
It was all going so well for the Dons until keeper Brown’s scuffed clearance from a Shay Logan pass back allowed Johansen to set up Griffths, whose angled-drive was saved by the keeper for a corner.
When Armstrong flighted the ball into a packed penalty area Denayer rose highest to head in, with the Aberdeen keeper again looking uneasy under pressure from Griffiths.
The first-half ended with Gordon punching a McLean free-kick over the bar for another Aberdeen corner which came to nothing.
Celtic should have doubled their lead in the 51st minute in a breakaway which saw the Aberdeen defence posted missing, but Johansen’s pass to Griffiths was over-cooked.
At the other end, a deep cross from wide by Pawlett was headed over by Considine.
Griffiths then had the ball in the net as Celtic broke again but this time the flag was up, albeit late.
However, the former Wolves player did not have to wait long until he got his counter.
When Dons defender Maark Reynolds clattered into the back of Johansen insided the penalty area, referee John Beaton pointed to the spot with Griffiths beating Brown with ease, before being immediately replaced by Guidetti.
The champions looked rampant and Brown saved an effort from Johansen before a low drive from the edge of the penalty area by the electric Mackay-Steven evaded his grasp, going in off the post.
Aberdeen’s resistance had all but evaporated. Guidetti cracked a shot off the outside of the post before Johansen converted an Adam Matthews cut back with 11 minutes remaining and in the end the scoreline could have been more depressing for the visitors.