A flying header from Dean Keates on the half-hour was enough to send the visitors home happy and confirm the step-up for Darren Ferguson's expensively-assembled side.
However, Hereford, thanks to MK Dons' victory at Stockport County, still have their fate in their own hands.
The Bulls remain in third place in the table knowing that three wins from their last three games will be enough to ensure promotion.
Peterborough made the early running and forced two quick corners neither of which came to anything.
Hereford took some time to settle but, on 15 minutes, Gary Hooper raced on to an astute pass from Sammy Igoe only to be driven wide and the chance was gone.
Clint Easton then drove a shot wide from 20 yards before Posh took the lead with a goal of the highest quality in the 29th minute.
Chris Whelpdale raced away down the right and delivered a perfect cross. Keates threw himself at the ball and sent an unstoppable header flying past Wayne Brown and into the top corner of the net.
Seconds after the interval an excellent save by Joe Lewis prevented Steve Guinan from grabbing an equaliser.
And the Peterborough keeper foiled Guinan again later in the half after the Bulls striker had been sent free by a good pass from Easton.
With Hereford pressing forward, there were always likely to be chances at the other end and it took a couple of excellent stops from Brown to prevent Craig Mackail-Smith from extending the lead.
After that, Peterborough were able to win control of the midfield and run the clock down before their ecstatic supporters spilled onto the field at the end to celebrate their promotion.