Chester edged closer to the Football League trap-door as Bournemouth's win eased their own relegation fears.
The Cherries led when Brett Pitman's inswinging free-kick avoided everyone, including keeper Jamie Spencer, and ended up in the back of the net.
Chester created pressure, and Kevin Roberts was within inches of levelling but could not reach a corner.
But Anton Robinson secured the win, finishing off from close range after Spencer had saved Liam Feeney's effort.
That leaves City, four points adrift of safety with a vastly inferior goal difference, needing to win their last two matches to stand even a chance of survival.
But a win at Aldershot on Saturday (25 April, 1500 BST) would at least keep them alive for another week, as Bournemouth and Grimsby Town, the only two sides they can catch, meet head on at Dean Court.
Chester: Spencer, Roberts, Linwood, Kelly (Jones 80), James Vaughan, Barry (Rutherford 59), Harris, Owen, Wilson, Lowe, Ellison (Partridge 46).
Subs Not Used: Mannix, Rule
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