Derby's first win in four matches ended Peterborough's unbeaten run in the npower Championship.
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Posh arrived at Pride Park as the division's form team having set a club record by going 10 games without defeat at this level but they struggled to live with the Rams until home goalkeeper Frank Fielding was sent off in the 62nd minute.
Substitute Grant McCann scored the resulting penalty after Fielding's dismissal but Darren Ferguson's side had fallen behind to goals from Craig Bryson, Chris Martin and Richard Keogh either side of half-time.
Huddersfield's win over Millwall earlier today saw Peterborough drop a place to 21st before kick-off and they are now only outside the relegation zone on goal difference.
Bryson, leading scorer Jamie Ward and fellow striker Conor Sammon were recalled to the Derby starting line-up, replacing Ben Davies, Kieron Freeman and Mason Bennett.
Meanwhile, midfielder Hughes, who celebrated his 18th birthday this week by signing a new contract with the Rams, was named among the substitutes after spending two months out with a groin injury.
On-loan Gillingham midfielder Jack Payne returned from injury for Peterborough in place of McCann.
Former Posh playmaker Paul Coutts' mishit cross that smashed against a post after two minutes put the visitors on the back foot and that is where they remained for the entire first half.
Derby dominated the first 45 minutes and would have gone into half-time thinking they should have been further ahead after failing to make the most of several sustained periods of pressure.
Martin dragged a shot wide before Sammon skipped past two defenders and curled a right-foot effort narrowly wide from just outside the box.
More good play from Sammon, who chased what appeared to be a lost cause to win a corner that resulted in Craig Forsyth flashing a volley just off target from what was Derby's 11th corner at the midway point of the first half.
Rams skipper Keogh headed over the crossbar at the far post from a Ward corner shortly after the half-hour mark and then Coutts saw a well-struck low shot repelled by Peterborough goalkeeper Robert Olejnik.
The hosts finally got the goal they deserved five minutes before half-time.
Ward and Sammon combined well down the left and the latter picked out Bryson in the box to blast the ball home from close range.
Posh threatened for the first time in first-half injury time when Dwight Gayle burst into the area and shot narrowly wide.
Visiting boss Ferguson made two changes at the break, introducing McCann and Nathaniel Mendez-Laing for Gaby Zakuani and Kane Ferdinand.
Perhaps Peterborough were still trying to reorganise themselves at the start of the second half as, come the 52nd minute, the scoreline was more reflective of what had preceded the interval.
Martin doubled Derby's lead with a superbly-taken powerful, low shot on the turn and then Keogh headed in a third goal when he was left unmarked at the far post after Forsyth had flicked on Ward's corner.
The Rams were cruising but they suffered a setback just after the hour mark when Fielding brought down Gayle, who was clean through on goal.
Fielding received a straight red card before McCann sent his penalty past substitute keeper Adam Legzdins, who was brought on at the expense of Martin.
After almost constantly being under the cosh until this point, it was now Peterborough's turn to put Derby under pressure.
Lee Tomlin had a good chance to pull another goal back after 73 minutes but he dragged his shot wide from 12 yards out.
Gayle then saw a shot blocked as Legzdins was called upon to make a save for the first time.
At the other end, a breakaway by the Rams resulted in Coutts' deflected shot looping just over the bar.
Sammon had a chance to finish off the game in the second of seven minutes of second-half stoppage time but he was denied by Olejnik.