The Russian struck twice in the second half and, although Will Hughes pulled one back 10 minutes from the end, Nick Blackman pounced deep in stoppage-time to leave Derby without a home victory in the Championship this season.
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.
Derby were moving the ball around confidently and in the 20th minute, Jamie Ward set up Hughes for a shot from the edge of the area which McCarthy held under his crossbar and Ward forced the keeper into a diving save to his right three minutes later.
McCarthy could only parry a stinging 30-yard drive from Ward in the 26th minute but there was a moment of danger for Derby three minutes later when Hal Robson-Kanu just failed to turn in Gareth McCleary's low cross from the right.
That sparked off a period of Reading possession but the visitors had still not forced Lee Grant into a save and the first half ended with McCarthy diving full length to his left to turn behind a 20-yard strike from Hughes.
But Reading were ahead in the 47th minute when a free-kick from Obita was headed down at the back post by Alex Pearce and Pogrebnyak hooked the ball in from inside the six-yard box.
The big striker pounced again in the 62nd minute when McCleary's cross bounced off Russell for the Russian to sidefoot past Grant from 10 yards.
Derby were struggling to break down a disciplined Reading defence but the home side gave themselves a chance with 10 minutes left when they finally found a way past McCarthy.
Reading failed to get the ball clear on the left edge of their area and Hughes created space to curl a shot across the keeper and inside his right-hand post.
It was the first goal Reading had conceded in 365 minutes and the home crowd sensed their team could get something out of a game that had looked to be all over only minutes earlier.
There was now a touch of desperation about some of Reading's defending as Derby's players buzzed around and a roar went up when the board showed six minutes of added time.
But it was Reading who scored again in the fifth of those when they broke away and Blackman slid the ball past Grant to wrap up an impressive victory.