Wales international Craig Morgan went after 28 minutes with his central defensive partner Ryan Bennett also seeing red card in first-half added time
Morgan received his marching orders from referee Nigel Miller after a two-footed challenge on County danger man DJ Campbell and it was he, on loan from Leicester City, who caused problems again.
As Campbell stormed into the area, Bennett, a club record signing £500,000 signing after making a loan move from Grimsby permanent, thought he had won the ball. County Durham official Miller had other ideas and pointed to the penalty spot before producing his red card again.
Goalkeeper Joe Lewis did his best to un-nerve Steve Davies as he stepped up, but the County man kept cool and opened the score dispatching a right-footed shot low into the corner of the net.
George Boyd's vision had helped rock bottom Posh to a lively start, the long-haired front man producing sweeping crosses that forced County to back pedal with Izale McLeod going closest with a low dive just wide of the far post.
McLeod, one of four loan signings paraded by Posh, had to be sacrificed after Morgan's dismissal, manager Mark Cooper sending on Charlie Lee to bolster the defence with the home side holding their own until disaster struck again resulting in Bennett's enforced exit.
It was almost academic for Derby in the second half with Campbell increasing the lead, beating Lewis at the second attempt after Paul Green squeezed the ball through - and Campbell pounced again for Derby's third, heading home unmarked from substitute Kris Commons' deep 75th minute centre.
Surprisingly, Posh's nine put pressure on County near the end with goalkeeper Stephen Bywater forced into action by Boyd before standing tall as Craig Mackail-Smith burst forward and hit a rising shot.