Dean Keates' winner took Peterborough a step closer to promotion.
The midfielder rose to head home Scott Rendell's 71st-minute assist after Rendell and Aaron Mclean had earlier missed chances to put Posh ahead.
Struggling Chester might have pinched a point with a late attack had Craig Morgan not thwarted John Murphy with a splendid last-ditch tackle.
Chester's Tony Dinning was sent off two minutes from time for a second bookable offence after he clashed with Keates.
Peterborough: Lewis, Gnakpa, Westwood, Morgan, Day, Whelpdale, Lee, Keates, Boyd, Mclean, Rendell. Subs Not Used: McKeown, Low, Newton, Hyde, Williams.
Goals: Keates 71.
Chester: Danby, Roberts, Kelly, Linwood, Wilson, Partridge (Mitchell 90), Hughes, Rule (Sandwith 78), Dinning, Rutherford (McManus 70), Murphy. Subs Not Used: Palethorpe, Vaughan.
Sent Off: Dinning (88).
Booked: Dinning, Rule.
Att: 6,457
Ref: Dean Whitestone (Northamptonshire).
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