Derek McInnes' side moved to within three points of leaders Celtic with victory but should have had the game won with a third goal by half-time, but the officials failed to spot Adam Rooney's effort had crossed the line - despite television replays showing it was well over.
The visitors went ahead in the sixth minute when Andrew Considine bundled a shot home from close range, and that lead was doubled less than two minutes later when Niall McGinn crossed for Ryan Jack to register his third league goal of the season.
Rooney's shot from 12 yards then hit the underside of the crossbar and bounced down over the line before coming back out, but the goal was not given.
Hamilton played the last half-an-hour with 10 men following a second booking for Jesus Garcia Tena and, after substitute David Goodwillie had seen an effort ruled out for offside, McGinn added a third two minutes from time.
