The home side started on the front foot with Rooney going close in the early stages before debutant Kenny McLean’s long-distance effort was saved by Antonio Reguero.
But Aberdeen got the reward for their early superiority on 12 minutes when Jonny Hayes whipped a dangerous cross into the box which was fumbled by Reguero and Rooney was on hand to sweep the ball home.
County’s Fillip Kiss tested Scott Brown from range moments later before Mark Reynolds saw his header saved by Reguero at the other end.
Joe Shaughnessy entered the field of play before the end of the first half, replacing Donervorn Daniels who was forced off due to injury.
Aberdeen came straight out of the traps in the second half and doubled their advantage in the 48th minute.
This time Rooney turned provider, feeding Pawlett who rounded the ‘keeper before coolly slotting the ball home from a very tight angle.
County tried to force their way back into the game with Kiss and Martin Woods both testing Brown from distance.
But Aberdeen extended their lead on the hour mark with a stunning effort from Logan who smashed the ball into the top-right corner from outside the area.
Aberdeen should have added to their lead through Pawlett but the midfielder was denied twice by Reguero.
But they did manage to add a fourth goal five minutes from time when Goodwillie latched on to Hayes’ pass before sliding the ball into the back of the net.
Aberdeen trail Celtic only on goal difference following the win at Pittodrie, though the champions have two games in hand over Derek McInnes’ side.