Ryan Edwards gave Craig Levein's side the lead early in the second half but Odsonne Edouard equalised from the penalty spot and the Frenchman ran clear to fire home the winning goal with eight minutes left to seal another domestic clean sweep for the Hoops.
Celtic announced after the game that Neil Lennon, who took over from Brendan Rodgers on an interim role, had been offered the manager’s job on a permanent basis.
The result also means that Aberdeen - who finished fourth in the Ladbrokes Premiership - will join Rangers and Kilmarnock in the Europa League qualifiers in July.
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