The Posh never relaxed their grip on the game after Aaron Mclean raced into the area to drill home his 16th goal of the season after only three minutes.
George Boyd released the ball to Mclean who calmly beat goalkeeper Peter Gulacsi with a low shot into the far corner.
Straight after the break George Boyd swept in a low cross to Craig Mackail-Smith but he turned the ball wide with only the Hereford keeper to beat.
Hereford however had a chance to level in the 64th minute but striker Steve Guinan fired inches over the crossbar from 12 yards.
Six minutes before the end Hereford appealed for a penalty when Febian Brandy was challenged in the area but the referee waved their appeal aside.