Darren Ferguson's men had dominated until two major errors in the space of three second-half minutes put a first away victory of the season on a plate for the visitors.
Andy Monkhouse (57) broke the deadlock after Micah Hyde inadvertently turned a Ritchie Humphreys cross into his path.
Disaster struck again in the 59th minute when Hartlepool substitute Richie Barker pounced on some dreadful dithering between defender Craig Morgan and highly-rated home goalkeeper Joe Lewis to double the visitors' lead with his first touch.
Posh battled hard to rescue a point and George Boyd halved the deficit with a smart finish 13 minutes from time, arrowing a shot into the bottom corner after Aaron Mclean had laid a Chris Whelpdale cross into his path.
But the home side could not score again in an exciting finish and were left to rue both their own errors and two strong penalty appeals which were waved away in the opening period.