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.
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.
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Appiah almost claimed his second of the afternoon 10 minutes before the break when he headed Jem Karacan's effort just wide.
Manager Steve McClaren sent his Derby players out five minutes before the beginning of the second half, but it was Reading who made the better start.
Appiah went close when fired Chris Gunter's low cross wide before Karacan almost snuck in behind the Rams' backline.
Michael Hector made it 2-0 on 72 minutes when he reacted quickest to a goalmouth scramble to side-foot home.
Bent was put clean through inside the final 10 minutes but he couldn't feed Chris Martin after he went round Federici who did well to narrow the angle.
Gareth McCleary then consigned the Rams to another season in the Championship when he netted from the penalty spot after Karacan had been brought down by Grant inside the final five minutes.