The Dons dominated the opening exchanges and it seemed only a matter of time before they hit the front.
However, United almost snatched an unlikely lead after 36 minutes as David Proctor got ahead of his marker and his header was turned away by Jamie Langfield.
Aberdeen broke upfield in the next minute and finally made a deserved breakthrough. Gary Dempsey and Barry Nicholson combined before Nicholson crashed in a shot which Derek Stilllie could only parry into the path of Darren Mackie, who knocked the ball home.
The Dons extended their lead after 47 minutes. A Nicholson free-kick from 25 yards bent over the defensive wall and into the top corner of the net past the despairing reach of Stillie.
Twenty minutes from time, the visitors were awarded a soft penalty when Russell Anderson was harshly adjudged to have upended Craig Conway. Robson dispatched the spot-kick into the corner of the net.
The home side were not to be outdone however as they immediately went up the other end of the field to score another fine goal. Richard Foster's excellent cross into the area was brilliantly fired home first time by Nicholson.