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Reading had won nine of their previous 11 games against Derby but came into the match with seven first-teamers missing, which meant a first league start for 19-year-old Jordan Obita.
The Royals had not conceded in 285 minutes of Championship football but their defence was almost breached in the eighth minute when Johnny Russell got in on the left and Alex McCarthy could only push out his low shot but Craig Bryson could not turn in the rebound.
The Russian striker found the net for the first time since January and although Will Hughes gave Derby hope, sub Nick Blackman secured Reading's 10th win in 12 games against Derby who have yet to record a home Sky Bet Championship victory this season.
Reading keeper Alex McCarthy kept the visitors in the game in the first half but Pogrebnyak pounced in the 47th minute after a free-kick was knocked down and the side-footed his second in the 62nd minute when Derby failed to clear a cross.
Hughes beat McCarthy with a curling shot in the 80th minute which was the first goal Reading had conceded in 365 minutes of Championship football but Blackman wrapped up the points in the fifth minute of stoppage time.