Cambridge United striker Danny Crow headed a last-minute winner to pile the pressure on bottom club Chester.
City, who learn on Thursday if they are to be expelled from the league for non-payment of debts, failed to make the most of several first-half chances.
Cambridge improved after the break and Chris Holroyd went close with a 30-yard strike that tested keeper James Danby.
Danby then parried a Sam Ives shot from close range, but could not save Crow's header from Robbie Willmott's cross.
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