After going two behind for the second home game in succession, through goals by Alexander Diamond and Darren Mackie for Aberdeen, Celtic staged a magnificent fightback.
Unlike their match against Hearts, the home team pulled one back before half-time when Stanislav Varga headed home.
John Hartson equalised early in the second half before Craig Bellamy struck a wonderful volley in the 57th minute which turned out to be the difference between the sides.
Celtic still had to survive one or two late scares especially with Bobo Balde looking nervous in the heart of their defence, but at the end of an amazing few days, they now find themselves five points clear of Rangers though the Ibrox side still have a game in hand.
If Rangers win that game against Dunfermline then it sets up an absolute cracker of an Old Firm game next Sunday.
Celtic threatened early on when Bellamy's cross to the near post was just intercepted by Michael Hart. Only a last-ditch tackle by Markus Heikkinen kept Joos Valgaeren out as the Belgian raced into the box after a one-two with Hartson.
Aberdeen shocked Celtic by taking the lead with their first attack. From Chris Clark's corner, Balde looked to have cleared the danger, but Kevin McNaughton quickly transferred the ball to Scott Severin whose cross was sidefooted home from ten yards by Diamond.
Richie Byrne was then booked for a blatant trip on Stilian Petrov and Alan Thompson's free-kick was cleared by the Aberdeen defence.
The Dons amazingly went two ahead when Scott Muirhead outpaced Neil Lennon down the left flank before firing in a low cross which the pacy Mackie reached before Valgaeren and Varga to place his shot past David Marshall.
Varga threw himself to concede another corner as the Celtic defence struggled.
Aberdeen goalkeeper Ryan Esson did well to race from his line to save at the feet of Petrov after Bellamy's clever flick had put the midfield player in space. The Dons keeper then punched out a high ball from almost under his bar as Hartson threatened.
From Thompson's corner, the ball was cleared only as far as Jackie McNamara who struck a sweet shot with the outside of his boot which Esson just managed to touch over.
From another Thompson corner Celtic thought they had reduced the deficit when Balde's header appeared netbound but McNaughton popped up on the line to head clear.
The Celtic opener was not long delayed as Aiden McGeady latched onto the clearance before curling in a cross which Varga glanced home from six yards.
This was the goal which Celtic desperately needed and it was noticeable that they started to stroke the ball about after this breakthrough.
Aberdeen still threatened though, and when Muirhead's cross ended on the top of the net, there was much relief in the Celtic defence.
Just before half time Hart foolishly pushed Bellamy in the back on the edge of the box but McGeady's free-kick was blocked by the wall.
At the start of the second half Aberdeen were pinned back in defence and Celtic were level by the 50th minute. Petrov was aware of Varga's break and fed the ball to him and when his pass was touched on by Hartson to Bellamy it looked as though the striker must score but Esson bravely blocked the Welshman's shot.
Aberdeen thought the danger was cleared but Didier Agathe, who had come on earlier for the injured Valgaeren, seized on Muirhead's weak pass to Byrne and crossed for Hartson to sweep the ball home at the near post.
The crowd were now at fever pitch, but when Balde carelessly lost possession it ended with McNaughton's curling shot going narrowly over.
Celtic went ahead for the first time when Petrov's deep corner reached the unmarked Bellamy beyond the back post and the striker showed tremendous technique by volleying high into the net.
Celtic thought they had gained a penalty shortly after when Byrne collided with Bellamy as they chased Sutton's clever pass but referee Craig Thompson waved away their claims.
With such a narrow lead Celtic could not relax and Muirhead's cross was just beyond Mackie and Richard Foster. From Foster's cross, Muirhead won a header at the back post but there was little power in it to trouble Marshall.
In the final minute Hartson's flick put Bellamy clear but the striker pulled his shot wide from a good position.
MAN OF THE MATCH: Craig Bellamy (Celtic) – The Welshman scored a fantastic goal and kept the Dons defence thinking throughout the 90 minutes with his trickery and searing pace.