Both of the Hoops’ opening two goals came against the run of play, with Jason Denayer heading in the first, while Leigh Griffiths netted the second from the penalty spot.
By the time Gary Mackay-Steven and Stefan Johansen had added further goals, the game had slipped away from the Dons, who ran out of ideas as well as any hope of avoiding defeat for the first time in the league since early November.
The first hour of the match at Celtic Park was keenly contested, with Aberdeen the more positive side for much of it.
First, Niall McGinn forced a good save out of home ‘keeper Craig Gordon before Kenny McLean headed off target when well placed.
And, with half-an-hour played, Ryan Jack’s 22-yard strike was too close to Gordon, who gratefully caught the ball as the visitors threatened again.
Celtic’s first real chance arrived in the 36th minute when Griffiths fired straight at ‘keeper Scott Brown, who blocked the ball away for a corner.
From the resulting set-piece, Celtic took the lead when Denayer leapt highest to nod in Stuart Armstrong’s corner from close range.
Shortly before the break, McLean tested Gordon with a 30-yard free-kick but the Dons were unable to find an equaliser which their first-half display had deserved.
The hosts should have added a second goal five minutes into the second half but, with the Aberdeen defence stretched, Johansen’s cross to an unmarked Griffiths was well overhit as the ball ran harmlessly out of play.
At the other end, Andrew Considine headed over when offered a great opportunity from Peter Pawlett’s deep cross.
On the hour, Jack was the next Dons player to miss the target, flashing a volley over the bar from the edge of the area.
And within two minutes Celtic had doubled their lead when Mark Reynolds clipped Johansen in the box and Griffiths coolly slotted home the penalty, sending Brown the wrong way.
Shortly after Griffiths had made it 2-0, the striker left the pitch to a standing ovation to be replaced by substitute John Guidetti.
From therein it was mainly Celtic, with Mackay-Steven making it 3-0 with a low strike that made good use of the right-hand post in the 69th minute.
Johansen was in the right place to side-foot the fourth goal 10 minutes from time, meeting Adam Matthews’ measured cross to net from 14 yards.
Aberdeen, who last lost in the league 16 weeks ago, are now six points adrift of Celtic and have played one game more.