Craig Mackail-Smith opened the scoring in just 20 seconds with further goals coming from Alan White and Gavin Strachan as the home side's confidence soared.
January capture Mackail-Smith forced a powerful header between goalkeeper Wayne Brown and the near post after meeting Jamie Day's cross at the end of a sweeping move straight from the kick-off, which also involved Shane Blackett and Peter Gain, without a Hereford man touching the ball.
Former Dagenham front man Mackail-Smith has now netted in five successive outings and then pulled the Hereford cover apart as Day curled over an inswinging right-wing corner that was headed home by quick thinking defender White for Posh's second on 13 minutes.
Hereford managed to stem the flow for a time after replacing Danny Thomas with Richard Rose and re-organising in defence and Steve Guinan gave Posh 'keeper Mark Tyler a few problems with a testing low drive just before the break.
Posh needed just three second half minutes to re-impose their authority. After a George Boyd centre caused problems, Phil Gulliver blasted a clearance straight at Strachan who managed to control the ball before firing into the net from close range.
Hereford carved out a few openings only for Guinan to fire wide from a cracking position and then the on-loan Cheltenham striker was penalised for hands after appearing for once to get the better or White.