Kgosi Nthe's 25-yard strike in the 13th minute put the League One side ahead before late goals from Grant McCann and substitute Nathaniel Mendez-Laing sealed the win at Rodney Parade.
It was only 19-year-old South African left-back Nthe's second goal in senior football as the ball squirmed under Newport goalkeeper Jamie Stephens.
The County stopper got injured in the second half and McCann's deflected shot in the 90th minute saw its way past substitute 'keeper Lenny Pidgeley before Mendez-Laing netted with almost the final kick of the game.
Justin Edinburgh's men created their own chances but Conor Washington, a former trialist at Peterborough, could not convert from David Pipe's supreme right-wing cross.
Then Robbie Willmott fired a shot from outside the penalty area on the stroke of half-time but Posh 'keeper Bobby Olejnik was equal to the effort.
League Two Newport huffed and puffed in the second half but could not find a way to break down the stubborn resistance of Peterborough before McCann and Mendez-Laing put the gloss on the victory.