The Hoops have been almost unstoppable this season with 'keeper Fraser Forster setting a new club record of 13 clean sheets in a row as Neil Lennon's side won 14 consecutive games.
This trend looked set to continue when Anthony Stokes fired Celtic into a ninth minute lead as he showed good control and skill to fire past Jamie Langfield.
However, the Dons arrived in Glasgow as the last side to score against the Hoops back in November and buoyed by their League Cup semi-final win over St Johnstone last weekend.
Adam Rooney diverted an Andrew Considine header on to the bar before Russell Anderson ended Forster's run of 19 hours and 23 minutes without conceding a goal as he volleyed Aberdeen level in the 38th minute.
Celtic then found themselves trailing in a game for the first time since November 2 when Peter Pawlett sent a superb angled shot past Forster in the 49th minute.
The Hoops haven't been defeated domestically since Morton knocked them out of the League Cup in September but couldn't find a way back into the game.
Virgil van Dijk missed a golden chance to head Celtic level and Rooney hit the post for Aberdeen as the Dons joined Rangers in the last eight to end any hopes of an Old Firm derby this season and the Parkhead club's hopes of a domestic double.
Celtic manager Neil Lennon was scathing about his team afterwards.
"I don't think I can single out any player apart from maybe James Forrest and Anthony Stokes who can come out the game with any credit at all," he said.
"We never really got a spell of pressure.
"We have been talking about the lack of goals scored against us this season but the problem today was the back four and midfield, who as two units were very poor."
Aberdeen manager Derek McInnes thought it had been a superb team performance.
"Everyone sacrificed a lot of themselves and worked extremely hard and had the resolve and attitude to come back from going a goal behind," McInnes said.
"We felt we could exploit then at set plays and thankfully we did that
I think it was a victory we more than deserved."
Celtic have got into the routine of scoring early goals this season and they didn't break the habit against the Dons.
Georgios Samaras, who had replaced the injured Charlie Mulgrew in the starting line-up, found Stokes with a beautifully flighted ball that the striker controlled superbly before firing the bal home through the legs of Langfield.
However, Anderson silenced Celtic Park as he began the first man to score past Forster in 1163 minutes of domestic football
The Hoops failed to deal with Barry Robson's corner and the ball broke to veteran defender Anderson who hooked a volley through the arms of Forster and into the roof of the net.
The Hoops, who were on a run of 14 straight wins on domestic duty, found themselves in very unfamiliar territory when they fell behind in the 49th minute.
Former Celtic player Robson played a perfect through ball for Pawlett who swivelled and sent an angled shot past Forster into the bottom right-hand corner to send the visiting fans wild.
Celtic had a chance to immediately respond when James Forrest ripped through the Aberdeen defence and sent over a superb cross into the box but the unmarked Van Dijk somehow managed to head over from six yards out.
Leigh Griffiths was handed his Celtic debut following his move from Wolves but couldn't help Celtic find a leveller.
Source : AFP
Source: AFP