On-loan Kwesi Appiah gave the visitors a perfect start when he broke clear of the Derby defence before calmly slotting home inside the first two minutes for his first Reading goal.
Raul Albentosa was appealing for a penalty when his shot struck the hand of a Reading defender, but the referee waved away the optimistic appeals.
Tom Ince went close for the Rams on 11 minutes when his curled effort was saved before Richard Keogh flashed a header wide.
Derby were almost level when Ince picked out Johnny Russell at the far post, but the latter couldn't find the target from close range before the half-hour mark.
Appiah almost claimed his second of the afternoon 10 minutes before the break when he headed Jem Karacan's effort just wide.
Darren Bent had a glorious chance to level in stoppage time when Russell was fouled inside the area, but the recalled striker saw his penalty saved by Adam Federici.