Gboly Ariyibi and Lee Novak scored early on whilst goals from subs Rai Simons and Ollie Banks in the second half wrapped up the win for Chesterfield.
FC United of Manchester headed home a stoppage time consolation through ex-Miller Luke Ashworth but by then the game was well won.
Dean Saunders gave a debut to on-loan Miller Richard Wood in the heart of the defence alongside Ian Evatt but there was no give to emotion as ex-FC United players Banks and Charlie Raglan were only named on the bench, but they both had pitch time after the break. Spireites had treated their National North hosts with great respect having watched them three times ahead of the tie at the 10 year old supporter- owned club who only moved to their purpose built £6.5m stadium six months ago.
United, managed by another former Rotherham United man, Karl Marginson, included the nephew of former Chesterfield boss John, Sam Sheridan who had a solid game in the engine room.
Spireites, who knew the winners of the tie would host League One leaders Walsall in the next round, made the sort of start the manager would have wanted, racing into a 2-0 lead with just 12 minutes played.
Former Manchester United player Sylvan Ebanks-Blake worked a bit of magic on the left side of the box to cross for Ariyibi to hit the target from 15 yards and before the crowd had settled Dan Jones delivered a cross, also from the left, for Novak to volley home from the near post with some style.
That early double allowed Chesterfield to play low-risk football and the two solid lines of four played high lines and forced United wide where they had little joy.
Before the break United saw centre forward Tom Greaves find a couple of openings, one he hit well wide and the other too weakly whilst Rory Fallon, Sheridan and Adam Thurston all managed efforts, Tommy Lee having to extend himself to block from the latter two players.
Sam Morsy came closest to making it three before the break, firing wide following on from a 50 yard burst forwards.
United switched to two up front after the break and looked a yard sharper but the tie was all but ended when Simons received from Morsy and beat the keeper in a one on one and as full-time approached, Banks took advantage of a slip by Ashworth to fire home from 25 yards; no celebration followed from the scorer.
Ashworth headed in late on to end the match on a positive note for the hosts who may not have wanted a Monday night match, but they hosted it with plenty of class.
Spireites will now look to take their impressive away form to the Proact as they host Oldham Athletic at the weekend looking to push further up the table in the bread and butter of the league.
FCUM: Carnell, Brownhill, Thurston, Stott, Lynch, Ashworth, Fallon (Daniels HT), Sheridan (Byrne 79), Greaves, Wright, Lindfield (Patterson HT). Subs: Wolfenden, Brown, Bayunu, Madeley.
Chesterfield: Lee, Talbot, Evatt, Wood, Jones, Ariyibi, Herd (Banks 55), Morsy (Raglan 71), O’Shea, Novak, Ebanks-Blake (Simons 56). Subs: Cairns, Dieseruvwe, Hird, O’Neil.
Goals: Ariyibi 6, Novak 12, Simons 68, Banks 87 for Chesterfield; Ashworth 90, for FC Utd
Ref: Oliver Langford (West Midlands).