Laurence Wilson gave Chester a perfect start in their FA Cup second round replay but Bury prevailed on the road. Wilson's mazy run ended in an opening goal on three minutes and Greg Blundell and John Walters had further chances.
But their failure to convert proved costly as Bury levelled before the break with Andy Bishop's fierce header.
Glynn Hurst's far post header from Marc Pugh's cross and a Dwayne Mattis shot threaded through a crowded box set up a tie at home to Ipswich for Bury.
Chester: Danby, Marples (Steele 59), Bolland, Artell, Sandwith (Linwood 52), Stephen Vaughan, Hand, Martinez, Wilson, Blundell (Semple 72), Walters.
Subs Not Used: Hessey, Westwood.
Goals: Wilson 3.
Bury: Fettis, Scott, Challinor, Woodthorpe, Brass, Pugh, Turnbull (Barry-Murphy 80), Mattis, Buchanan (Kennedy 90), Bishop, Hurst (Speight 75).
Subs Not Used: Grundy, Youngs.
Goals: Bishop 36, Hurst 48, Mattis 54.
Att: 2,810
Ref: D Foster (Tyne & Wear).