The striker was on target in the 19th and 33rd minutes to help the Dons inflict a first home loss of the campaign on the Tangerines.
The writing was on the wall as early as the seventh minute when Niall McGinn’s deflected shot from outside the box landed on top of the crossbar.
Rooney’s opener, which arrived 12 minutes later, came courtesy of an error by United goalkeeper Radoslaw Cierzniak who failed to hold on to a David Goodwillie header and the Irishman took advantage from close range.
His second was a more clinical affair after Andrew Considine’s cross to the far post was nodded back into Rooney’s path by Ryan Jack.
The visitors almost added a third before the break when McGinn struck woodwork for a second time, with the midfielder lashing the ball off the inside of a post.
Aberdeen also enjoyed the better chances in the second half with Goodwillie firing narrowly over and Peter Pawlett being denied by Cierzniak who turned his effort over the bar.
The win moves the Dons level on points with third-placed United who remain ahead in the table by a single goal.