The home side started on the front foot and fired an early warning shot when new signing Kenny McLean picked out Rooney inside the box, only for the striker to shoot wide.
McLean looked fired up on his debut and almost got his name on the scoresheet in the 11th minute as his shot from the right was saved by Staggies goalkeeper Antonio Reguero.
Reguero was at fault one minute later when the Dons took the lead, fumbling a cross from Jonny Hayes to allow Rooney an easy tap in.
The home support cried out for a penalty on the stroke of half time when Shay Logan went over in the area, but referee Craig Thomson waved away the Aberdeen's protests and the scoreline remained 1-0 until the second period.
Peter Pawlett claimed Aberdeen's second just six minutes into the second half, racing inside the box and beating Reguero from a tight angle to put his side further in front.
The hosts were out of sight just after the hour mark when Logan added a peach of a third, finding the top corner from outside the box to bury County.
Aberdeen's fourth came through substitute David Goodwille, who calmly slid the ball home after a deft pass from Hayes sliced the County defence in half.
The result leaves the Dons behind league leaders Celtic only on goal difference, but the Hoops have a pair of games in hand.