Second-half goals from on-loan midfielder Dean Furman and Michael Boulding gave the visitors a win they thoroughly merited against a Chesterfield side that was missing a number of key players through injury and suspension.
It now remains to be seen if Chesterfield manager Lee Richardson, who is out of contract next month, will be there next season but Bradford boss Stuart McCall can certainly look ahead to trying to take his club a stage further.
On the evidence of this performance, much will depend on whether he can retain the services of Furman and Nicky Law who were instrumental in this victory.
Law had been a real threat to Chesterfield in a first half which contained plenty of openings but Bradford's finishing did not match the approach work.
Boulding's brother Rory, making his first appearance for Bradford, had a shot deflect behind for a corner and Joe Colbeck wasted a great chance when Law put him through in the 29th minute.
Lee Bullock headed wastefully wide from eight yards and Chesterfield had to wait until the 38th minute when a low shot from Drew Talbot forced Jon McLaughlin into action for the first time on his debut.
Those missed openings could have proved costly but Bradford were ahead in the 54th minute when Law got to the by-line on the Chesterfield right and played a low cross into the path of Furman who stabbed home his fourth goal for Bradford.
Chesterfield had Bradford under pressure for spells without really carving out a genuine chance until the 78th minute when Talbot should have equalised.
The striker beat the offside trap but he shot well wide as McLaughlin came off his line and two minutes from time Boulding showed him how to finish when he smashed in a shot from 10 yards after an effort by Kyle Nix had been deflected into his path.