Craig Mackail-Smith's penalty five minutes from time added to an 80th minute strike from Aaron McLean helped Posh overturn Chester's first-half lead.
The home side were left to rue a host of missed chances which allowed Darren Ferguson's men to stay in touch and then snatch the points late on.
On 21 minutes, Kevin Ellison was within a whisker of giving Chester the lead when his low left-footed strike from 20 yards caught the outside of the post with keeper Mark Tyler well beaten.
The opener came in the third minute of first-half added time. John Murphy rolled the ball across the edge of the box where Mark Hughes arrived to rifle a low shot into the back of the net.
The visitors had an appeal for a penalty turned down four minutes after the restart when Mackail-Smith went down under a challenge from Kevin Sandwith.
Christ Westwood should have levelled matters but headed wide and, at the other end, Ellison had a chance to double the lead but the ball came to him on his weaker right foot and he volleyed wide.
A mis-hit cross from the right flank by Paul Rutherford had Peterborough keeper Tyler struggling and he was fortunate as the ball hit the foot of the post and went away to safety.
A swift break up field by Rutherford saw him set up Ellison with a shooting chance, but the midfielder's well struck shot was wide of the target.
On 71 minutes a mix-between Chester defenders Paul Linwood and Paul Butler, who both left the ball to each other, allowed Mackail-Smith a clean run on goal, but the striker's side-foot effort was saved by John Danby.
A lengthy period of pressure by the visitors finally paid off on 80 minutes when McLean pounced on Linwood's poor defensive header to fire the ball home from eight yards out.
And five minutes from time a poor challenge by Kevin Roberts on substitute Jeff Hughes allowed Mackail-Smith the chance to snatch victory.