Aberdeen 1 Celtic 3
The win means that they go to arch-rivals Rangers next Saturday leading the race for this season's Championship.
Aberdeen produced a spirited first-half display and went in front thanks to Chris Maguire's header. But once Celtic got back on terms there was only going to be one winner.
Aberdeen should have gone ahead on four minutes. Celtic's centre-backs were caught square when a Mark Kerr throughball allowed Maguire to race clear.
However, with the goal at his mercy, he scooped the ball over Artur Boruc and the effort bounced wide of the upright from 14 yards.
At the other end Jan Vennegoor of Hesselink and Scott McDonald combined, only for the diminutive striker to drag his 22-yard left-foot effort wide of the target.
Celtic went close once again on 11 minutes. McDonald raced down the left before picking out Aiden McGeady on the edge of the area. His curling effort beat Jamie Langfield in the Dons goal but flew narrowly wide of the post.
Aberdeen went ahead on 22 minutes when Maguire stole across Lee Naylor to gleefully head Charlie Mulgrew's free-kick past Boruc.
The Dons were in the ascendancy, with Maguire and Tommy Wright combining before the youngster raced away from Steve McManus and crashed in a great shot from the angle which was blocked at the expense of a corner by Boruc.
From the resulting corner Scott Severin fluffed his lines as he drove the ball into the ground and over the bar when it appeared easier to score from six yards.
Celtic came close to getting back on terms on 27 minutes. McDonald played in Paul Hartley and his dipping 23-yard left-foot volley was brilliantly turned over by Langfield.
Celtic drew level on 45 minutes. Shunsuke Nakamura's free-kick was headed goalwards by Gary Caldwell only for Andrew Considine to deflect the ball past the despairing grasp of Langfield and into the net.
Celtic were dealt a blow in the 49th minute when skipper McManus failed to run off an early knock and had to be replaced by Glenn Loovens.
Celtic went close to taking a 55th-minute lead when McGeady and Naylor worked a clever one-two. The full-back's shot deflected off Severin, only for Langfield to acrobatically tip the ball over.
Aberdeen wasted a magnificent chance in the 58th minutes. Mulgrew's throughball found Wright, who raced between Loovens and Caldwell.
However, with the goal at his mercy, the striker took too long to get his shot away allowing Caldwell to make a brilliant last-ditch block.
On 64 minutes a clever Marc Crosas cross found Hartley just behind his marker at the far post but his header was excellently turned over the bar by Langfield as the visitors continued to press.
The visitors scored a great goal to edge ahead on 72 minutes when Andreas Hinkel's early ball across the area was brilliantly swept home from 12 yards by Aussie striker McDonald.
Celtic ought to have made the points safe on 80 minutes. McGeady played McDonald in on goal but Langfield forced the striker wide and the chance was lost.
With the Dons chasing a late equaliser they were caught out at the back in stoppage time. A long ball out of defence saw McDonald out-muscle Andrew Considine before smashing the ball home through the legs of Langfield.