The visitors were stronger and quicker than Derby throughout and could have won by a bigger margin.
Joao scored a Carabao Cup hat-trick last weekend and he followed his smart finish by setting up Ejaria as well as hitting the woodwork in the second half.
Rooney had not been fit enough to start and watched from the bench as Reading began brightly on a breezy afternoon.
Michael Olise made a threatening run across the face of the Derby box but his pass to Joao was easily cut out and the home side had the first attempt on goal when Jack Marriott's shot was deflected behind in the 11th minute.
It was a big chance for the visitors who had been quicker to the ball with Derby limited to shots from distance and Reading made no mistake with their next opportunity in the 40th minute.
After Derby conceded a corner, Olise's low delivery to the near post caught Derby out and Joao reacted quickly to side foot in from six yards.
Joao was involved again as Reading made it two in first half stoppage time, holding up the ball before a clever back heel set up Ejaria who fired across Marshall and inside the far post.
The second half began on a farcical note with substitute Nathan Byrne booked on debut because Derby had not told the fourth official they were bringing him on.
At least Derby had a shot on target with Morgan Whittaker forcing Rafael Cabral into a save but Reading should have scored again when Swift broke clear in the 55th minute but took the ball too close to Marshall.
Joao rattled the crossbar two minutes later and it was no surprise when Rooney was brought on in the 63rd minute.
Despite Rooney's presence, Derby were still struggling to make an impression on Reading who finished the game as they began, in control, and although Marriott did test Cabral in the final seconds, it could not disguise a poor afternoon for the home side.