A first half penalty set Chester on their way and two second half goals secured the win, although Chester were grateful at times for some excellent saves by keeper Chris MacKenzie.
The Posh should have taken the lead in the 12th minute as Trevor Benjamin wasted two good chances when barely four yards from goal, his first effort being saved at point-blank range by MacKenzie, and then the fired the rebound over when it looked easier to score.
Chester had a good opportunity five minutes later when Ryan Lowe broke to the edge of the box, but failed to spot the unmarked Michael Branch, who would have been through on goal had the striker seen his run.
The referee's assistant came to the aid of Peterborough on 25 minutes when Ben Davies fired the ball home, but the effort was ruled offside.
Chester's pressure finally paid off ten minutes before the interval as Branch was taken down by keeper Mark Tyler after beating the offside trap, gifting a penalty.
Tyler received only a yellow card for his misdemeanour and was beaten from the spot kick taken by Branch, despite going the right way.
For the visitors Mark Arber was holding his head in his hands when his goal bound strike was superbly saved by MacKenzie five minutes from the break.
The advantage was doubled eight minutes after the restart as a cross from Branch was not dealt with by the Posh defence and Stewart Drummond rifled the ball in from eight yards out.
The visitors should have given themselves a lifeline moments later when Peter Gain was clean through, but MacKenzie proved equal to the task with another fine save.
The points were well and truly wrapped up on 66 minutes as Lowe hit a goal of the season contender with a thunderous strike from the corner of the penalty box which flew past Tyler.
Ryan Semple's strike 15 minutes from time proved only a minor consolation for the visitors.