This victory put the visitors 22 points clear at the top of the table and only requiring a further three wins to become champions again.
Following the game, Dons manager Jimmy Calderwood expressed his disappointment at losing the opening goal when he said: "We tried to play for offside, but we have so much pace we don't need to do it. All credit to (Craig) Beattie, who finished well."
For the second goal he went on to say: "You know how good (Shunsuke) Nakamura is with his free-kicks, he scored like that against much better teams than us, this gave us a mountain to claim."
Gordon Strachan praised his Bhoys afterwards, adding: "The team were smashing, it was a right good game of football and we are very, very happy."
On eight minutes excellent lead-up play between the Dons twin strikers Lee Miller and Steve Lovell saw the latter break clear of McManus but Pressley was on hand to clear the danger.
Nakamura's long ball into the channel caught Aberdeen's rearguard napping on ten minutes with the home side looking for offside. Beattie raced clear and smashed the ball beyond Jamie Langfield from the angle to Celtic an early lead.
Celtic took control of the game on 19 minutes. Russell Anderson was harshly penalised for a pull on the jersey of Jan Vennegoor of Hesselink on the edge of the area. From the free-kick Nakamura made his usual immaculate job by planting the ball into the top right-hand corner of the net.
It should have been three for the visitors in 28 minutes, Paul Hartley burst into the Dons box, teeing the ball up for Beattie, but from 12 yards he fired wildly over.
On 42 minutes the home side came close to reducing the deficit when Lovell should have done much better than head a Richard Foster cross wide of the upright.
The Dons came close again minutes later. Stephen McManus's half-cleared header fell into the path of Barry Nicholson, whose tremendous volley from the edge of the area was just too well struck and flew narrowly over the bar.
In stoppage time a Scott Severin mis-kick fell into the path of Chirs Clark whose snap shot from 16 yards looked goal-bound until Artur Boruc somehow twisted in mid-air and turned the ball round the post.
Aberdeen were on the offensive straight from the re-start, the best chance falling to Anderson, who rose above his marker to meet a Nicholson corner in 50 minutes, the ball was too close to Boruc who held the ball low down to his right.
In 54 minutes excellent link-up play between Jiri Jarosik and Vennegoor of Hesselink saw the big Dutchman thread the ball through to the midfielder, whose lob was just parried away by Langfield.
At the other end McManus was booked for dragging down Miller as he turned on the edge of the area. From the resultant free-kick Nicholson's goalbound effort was blocked unintentionally by Anderson.
Severin was given space around 25 yards out on 71 minutes, but a fantastic finger-tip save by Boruc kept the visitors a clean sheet.
As the home side continued to press they spurned another great opportunity in 77 minutes. From a Chris Maguire corner the unmarked Miller could only head wide with the goal at his mercy.
Aberdeen's persistence paid off after 90 minutes when a long Langfield clearance was knocked on by Miller into the path of Mackie, who sped away from McManus before slotting the ball beyond Boruc for a consolation.