The in-form Hoops Leigh Griffiths striker headed the home side ahead just before the interval then scored from the spot in the 53rd minute to take his season's tally to 16, with James Forrest adding a third before Adam Rooney scored a late consolation for the visitors.
Boss Ronny Deila had rounded on his "jealous" critics on Friday, most of whom had questioned his record in Europe - Celtic are bottom of their UEFA Europa League section after their recent defeat in Molde - but domestically they remain without equal.
The Granite City men have now failed to win any of their last five league games and it is difficult to make a case for them returning to mount a challenge to the champions, who were still without skipper Scott Brown through a knee injury.
Left-back Kieran Tierney and Socceroos midfielder Rogic came in for Emilio Izaguirre and Stuart Armstrong respectively, while Dons defender Andrew Considine replaced Peter Pawlett who dropped to the bench.
The first close call came on 10 minutes when Griffiths turned Aberdeen right-back Shay Logan before dragging his shot just wide of the far post.
The Pittodrie men, however, looked purposeful on the break and Rooney came close twice with flicks from crosses, first from Niall McGinn and then from Jonny Hayes.
In the 23rd minute Considine, appearing to be suffering from a head knock picked up earlier, was replaced by Paul Quinn, moments before Rooney had the ball in the Celtic net only to be ruled offside.
A minute later, a Hoops' appeal for a penalty was ignored by referee Willie Collum when Tierney's cross from the left was deflected behind by Logan, the official settling for the award of a corner.
Griffiths should have scored when he was left with only Danny Ward to beat from 10 yards but the Dons keeper saved at the expense of a corner which came to nothing.
In the 35th minute, after some more neat counter-attacking play by the visitors, the unmarked Rooney headed a Hayes cross past the post from the middle of the goal when he ought to have at least tested keeper Craig Gordon.
Four minutes later a Dedryck Boyata header from a Kris Commons corner came off the bar with the help of Dons midfielder Kenny McLean before being cleared for another corner which was defended.
It looked like Aberdeen would get to the interval level but in the 44th minute, Griffiths leapt highest in the penalty area to head a Tierney cross past Ward and change the complexion of the match.
There was time for Rogic to draw a shot wide of the far post before the whistle blew and it was the Australian midfielder who tested Ward with a powerful long-distance drive five minutes after the restart, before Commons missed the target from 14 yards.
Griffiths' second came when defender Ash Taylor clumsily crashed into Commons just inside the box, with the Scotland striker gleefully thrashing the spot-kick low past Ward.
The Dons had no option but to push forward but on the hour mark they were punished again when Forrest latched on to a Rogic pass and knocked the ball past Ward from 12 yards.
The goal deflated Aberdeen further and it looked a case of how many more Celtic could rack up.
Griffiths, Armstrong - on for Forrest - and Commons had further attempts on goal while in between Gordon made a great goal-line save from Aberdeen substitute Pawlett, on for Ryan Jack.
Rooney headed a Hayes free-kick past Gordon with two minutes remaining but by then Celtic had probably turned their attention to the return game against Molde at Parkhead on Friday (AEDT).
With Griffiths in such fine form, their Europa League hopes might not yet be over.
Elsewhere, St Johnstone survived a late fightback from Hamilton to win a six-goal thriller 4-2 at New Douglas Park.
Two goals for Graham Cummins and one apiece from David Wotherspoon and Michael O'Halloran put the visitors in control before Jesus Garcia Tena struck twice in the final nine minutes to offer some consolation.
St Johnstone are now fourth thanks to Ross County's 1-0 defeat away to bottom-club Dundee United, who secured their first victory under manager Mixu Paatelainen thanks to a late penalty from Billy Mckay.
Ten-man Inverness Caledonian Thistle came back to draw 1-1 with Dundee thanks to Greg Tansey's penalty, while Louis Moult's 87th-minute strike saw Motherwell snatch a 1-0 win away to Kilmarnock.
