The hosts took the lead somewhat against the run of play after 26 minutes when Mustapha Dumbuya's terrific cross was powered home by Magpies skipper Dean Leacock.
However, the lead did not last long as Posh captain Tommy Rowe replied in kind, glancing in a Lee Tomlin corner to make it 1-1.
Posh, who triumphed 5-1 at Colchester in the Capital One Cup in midweek, took the lead in the 54th minute as Rowe slipped in Tyrone Barnett, who had time to control and stroke the ball past Bartosz Bialkowski.
The visitors stretched their lead further after 58 minutes when Grant McCann cheekily chipped home a penalty after Mark Fotheringham had upended Tomlin.
After County had been denied a clear penalty for handball, the game was effectively over in the 71st minute when a defensive lapse saw Britt Assombalonga smash the ball home.
The hosts finally did receive a spot-kick for handball in added time, which allowed substitute Yoann Arquin to score, but it was too little, too late as the Magpies fell to back-to-back league defeats.