Second-half goals from Dean Furman and Michael Boulding sealed victory as the Chesterfield fans turned on their boss Lee Richardson.
Both sides had narrowly missed out on the play-offs but it was Bradford who looked more likely to score in an open first half.
Joe Colbeck and Lee Bullock missed excellent chances before Chesterfield's Drew Talbot went close with a low shot that Jon McLaughlin saved in the 38th minute.
The home fans were calling for the sacking of Richardson, whose contract is up this summer, when Bradford went ahead in the 54th minute through Furman who turned in a cross from Nicky Law.
Chesterfield had a great chance to level in the 78th minute when Talbot beat the offside trap but shot well wide and 10 minutes later, Boulding smashed in Bradford's second.