The midfielder netted either side of half time before Mickael Antoine-Curier capped off the scoring in stoppage time to send the surprise pacesetters four points clear at the top of the Scottish Premiership table.
The hosts opened the scoring on 15 minutes with the first clear-cut opportunity of the game, as Dougie Imrie lifted the ball over onrushing Dons keeper Jamie Langfield to allow Andreu to convert into the empty net.
The two strikers combined for the away side's best opportunity of the first half as Goodwillie crossed for Rooney, who scuffed his shot and allowed the recovering Hamilton defenders to scramble clear.
That proved to be Aberdeen's best spell of the match as Hamilton dominated the second half, taking only six minutes to extend their advantage as Andreu finished a well-worked move involving Daniel Redmond.
Hamilton limited the Reds to set-piece chances in their bid to launch a comeback, although Niall McGinn twice came close with dipping free kicks before Antoine-Curier made completely sure of the points.
The striker smashed home an Ali Crawford cross from close range for his fifth goal of the season to secure Alex Neil's side a 10th victory of the campaign in all competitions and leave Aberdeen seven points adrift.