Adam Rooney, whose decisive kick in the penalty shoot-out won last season’s final, scored the only goal of the game at Pittodrie after 25 minutes.
Hamilton had survived a couple of scares before Niall McGinn delivered a free-kick into the penalty area where the unmarked Rooney sent his diving header past Michael McGovern.
The Accies keeper had come to his side’s rescue to deny McGinn earlier when Rooney slid the ball the midfielder in the box after a swift counter-attack.
Peter Pawlett then exchanged passes with Irishman and had his shot turned round the post by the keeper, who produced an even better save moments later after McGinn’s cross deflected off Martin Canning.
Shortly after the break McGovern was back in action to keep out a goal bound effort from Andrew Considine with a one-handed save.
And three minutes later the Dons work a neat free-kick when ended with McGovern thwarting Pawlett.
But Accies had chances as well and Canning just failed to make contact with a cross in front of goal shortly before Scott Brown denied Tony Andreu.
And Dons keeper Brown made another diving save to thwart Andreu with the game moving into the latter stages.