CHESTER suffered defeat after giving their opponents a 2-0 lead for the third successive match.
James Armson and Lee Fowler scored two goals in a three minute spell to hand the home club a 2-0 lead after 24 minutes.
Substitute Craig Hobson made it 2-1 five minutes after the break, but substitute Marcus Barrington extended Nuneaton lead in the 80th minute.
Hobson netted once more towards the end of the match, but Chester failed to achieve an equaliser despite a battling display.
The Blues made just one change from Tuesday Night's 4-2 victory at Dartford, with midfielder Danny Harrison replacing suspended Kingsley James.
Chester started brightly, but Craig Mahon's second minute effort flew over the bar from the edge of the area.
And John Rooney's fourth minute shot was deflected into the possession of home keeper Christian Dibble.
Nuneaton countered with Anton Brown producing an overhead kick that bounced inches wide of the left post, and then pressed the Blues by winning three successive corner kicks.
Rooney responded in the 16th minute with a 30 yard drive that Dibble did well to paw round his right post.
But Nuneaton then broke the deadlock and found themselves 2-0 up after netting twice in a three minute spell.
James Armson volleyed home from 12 yards in the 21st minute after Adam Dawson's right wing delivery had only been half cleared by Matty Brown.
And Lee Fowler made it 2-0 in the 24tn minute with a 25 yard free kick which flew beneath Jon Worsnop.
Armson continued to press for the home club in the 26th minute, but he saw his goalbound effort saved by Worsnop.
Chester were missing the drive and presence of James in central midfield as Nuneaton were winning far more possession in central areas of the pitch.
Dawson connected with a 25 yard volley in the 28th minute as Nuneaton continued to enjoy lots of possession.
But Chester could have reduced their arrears in the 35th minute when Matty Hughes dissected the home defence to find Rhys Oates, but his shot from close range was saved by Dibble.
Dawson responded with a corner that picked out Theo Streete but his header was saved by Worsnop.
Rooney and Sean McConville both saw shots blocked and deflected towards the end of a frustrating opening half for the Blues.
But Chester looked determined to hit back in the second half after Ibou Touray and Craig Hobson had replaced Gareth Roberts and Danny Harrison at the break.
Hobson reduced the Blues arrears in the 50th minute with a superb glanciong header from Oates' right wing cross after a fine forward pass by Rooney.
And Hobson came with a whisker of equalising seconds later when another glancing header off a Hughes delivery flew inches wide of the right post.
Nuneaton steadied the ship with Dawson forcing Worsnop into a fine save.
But Chester still looked dangerous, with Rooney's 25 yard free kick being pushed round the post by Dibble, and Brown heading over from a McConville corner.
Oates also cut through the home defence, but his low shot was parried behind by Dibble.
Nuneaton extended their lead 10 minutes from time when substitute Marcus Barrington smashed home from close range after Dawson had delivered a right wing cross.
But Hobson made it 3-2 two minutes from time with a close range header from McConville's left sided corner.
Hobson came close to levelling matters in the 90th minute, but his close range shot was brilliantly saved by Dibble.
NUNEATON TOWN (4-4-2): Dibble, Starosta, Streete, Charles; Franklin; Armson, Dawson, Brown, Fowler (Smith 89); Gash, Sodje (Barrington 60). Subs (not used): Cowan, Stankevicius, Quinn.
CHESTER (4-3-3): Worsnop, Roberts (Touray 46), Charnock Brown, Kay; Harrison (Hobson 46), Rooney, Mahon; McConville, Hughes, Oates. Subs (not used): C Roberts, Peers, Menagh.
REFEREE: Paul Rees (Bristol).
ATTENDANCE: 973 (241 from Chester).