Ash Taylor, Niall McGinn and Adam Rooney were all on target for Aberdeen, while Hamilton finished the game with 10 men after Jon Routledge was dismissed.
Accies were undone on 28 minutes when Taylor powered the ball high into the net from close-range from a McGinn corner.
And McGinn doubled the lead six minutes after the break when he found the bottom-left corner from outside the box.
The Dons secured the points four minutes later when Rooney slotted home a spot-kick after Jonny Hayes was fouled by Grant Gillespie.
The visitors attempted to hit back quickly after the first goal and Scott Brown was forced to get down to his left to deal with a Tony Andreu shot.
Hamilton ‘keeper Michael McGovern then got behind a drive from McGinn and Ross Jack later sent a shot narrowly wide of the post as the first half came to a close.
Aberdeen twice came close to adding a fourth goal with David Goodwillie and Taylor both forcing saves from McGovern inside a minute.
And the Accies ‘keeper then tipped a McGinn shot over the bar after the Irishman was set up by Peter Pawlett.
A miserable day for Hamilton was completed eight minutes from time when Routledge was dismissed by referee Brian Colvin for an off-the-ball incident.