Barry Fry's men were made to work for the victory, however, despite opening up a two-goal lead inside 30 minutes.
Former Sheffield United and Birmingham City midfielder Curtis Woodhouse (pictured) opened Posh's account on ten minutes, and Richard Logan doubled the advantage on 28.
However, with the hosts seemingly cruising, Paul Riley pulled one back just before the interval and then stunned the home crowd with a second two minutes after the restart.
But with County having gained a foothold, Peterborough responded again and regained the lead with a David Farrell strike on 56 minutes.
County attempted to restore the equilibrium, but as they pushed forward were undone by two late goals.
Ex-Ipswich hit-man Logan grabbed his second with ten remaining, and the scoring was completed by Andy Clarke just three minutes later.
