Ross O'Donoghue gave the Dons a first half lead before the home side levelled matters. However Drew Jarvie's charges were in determined mood and went ahead again before the interval courtesy of a Scott Michie strike.
Further second half goals from substitutes Richard Buckley and Scott Muirhead ensured the long journey home was a happy one.
The only blemish on the night for the side was a head injury to centre back Robbie Hedderman which saw him exit the match in the first period.