But for once Celtic's form deserted them and a 38th minute equaliser from Russell Anderson and an angled drive by Peter Pawlett five minutes into the second half gave the Dons victory.
It was their first win at Celtic since they beat them in a Scottish Cup quarter-final six years ago.
Celtic, who have won the Scottish Cup a record 36 times, had not conceded a goal at home for 12 matches and had not lost a domestic match since September when Morton beat them in the League Cup.
Celtic, champions for the last two seasons, have won 21 and drawn three of their 24 Premier League matches and lead the standings by 21 points from Aberdeen, who are second.
(Reporting by Mike Collett; Editing by Ken Ferris)
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