Anthony Stokes gave the holders an early lead but goals from Russell Anderson and Peter Pawlett either side of the break saw Aberdeen deservedly into the quarter-finals.
Georgios Samaras’ chipped pass found Stokes (9) surging down the inside-right channel and the Celtic foward took a deft first touch before drilling the ball through Jamie Langfield’s legs.
However any home fans’ thoughts that this would turn into another stroll were swiftly disabused as Aberdeen, galvanised by Barry Robson and Jonny Hayes, began to find their feet.
Andrew Considine’s header was flicked on by Adam Rooney but the ball was somehow deflected over the bar before the Dons earned their just reward after a series of corners.
The ball broke kindly for Anderson (38) from Robson’s delivery and the defender hooked past Fraser Forster from six yards; the Celtic goalkeeper conceding for the first time in a domestic game since November.
Rejuvenated Aberdeen began the second-half as they ended the first and when Robson teed up Pawlett (50) he calmly steered an angled drive across Forster.
Virgil van Dijk planted a free header over from six yards moments later but he and his fellow defenders were again all at sea as another scramble ended with Pawlett hitting the upright from six yards.
Leigh Griffiths was thrown into the fray for his Celtic debut and but there was more graft than guile in the home side’s increasingly desperate attacks.
The ever-willing James Forrest did set up Griffiths but the new boy fired wide from 16 yards as Aberdeen – to the delight of their 3,000 supporters – saw out the three added minutes with few alarms.