David Zdrilic wrecked Celtic's 77-match unbeaten home record with a superb injury-time strike.
Zdrilic struck a left-foot shot past David Marshall to end Celtic's hopes of going through the league campaign unbeaten.
Henrik Larsson gave Celtic a first-half lead but second-half goals from Bryan Prunty and Zdrilic rocked Celtic Park.
A minute's silence was observed before kick-off in honour of former Celtic and Scotland goalkeeper Ronnie Simpson who died earlier in the week.
Aberdeen were without nine first-team squad members due to injuries and Steve Paterson was forced to name a youthful line-up.
The Dons packed their defence in a bid to frustrate Celtic but the home side were in control from the start.
It was no surprise when Larsson put the champions ahead after 15 minutes with his 36th goal of the season.
Aberdeen goalkeeper David Preece was badly at fault when he hesitated after Momo Sylla had flicked the ball on and Larsson had all the time in the world to stroke home a left-foot shot.
Aberdeen had their chances and won a string of corners but Scott Muirhead shot carelessly over the top with the Celtic defence hesitant.
The Dons lost Steve Tosh with a calf injury midway through the first half but it did not discourage them and Paul Sheerin forced a good save from Marshall with a long-range effort.
Celtic hit back and Neil Lennon thundered in a shot which Preece did well to beat out with the Aberdeen defence in disarray.
The lively Ross Wallace then tried his luck from 25 yards but it was directed straight at the Aberdeen goalkeeper.
Preece made amends for his earlier slip when Larsson eluded the Aberdeen offside trap again five minutes before the break and the goalkeeper got down swiftly to block the striker's shot.
Aberdeen stunned Celtic with an equaliser ten minutes into the second half when substitute Bryan Prunty took advantage of a wonderful cross from Muirhead to beat Marshall with a crisply-struck shot.
It prompted a predicable response from Celtic as they swarmed forward. Larsson sent a header narrowly wide and substitute Liam Miller swiped a shot at goal that Preece dealt with well.
Miller then saw a shot cleared off the line by Craig Higgins after more indecision from Preece as Celtic turned the screw.
Then came Zdrilic's goal that ended an unbeaten home record that had lasted since August 2001.