The slow-starting Bantams were hit by an early double whammy, but they kept their heads to claw themselves back into the contest before Barry Conlon wrapped up the win with a second-half penalty.
City were caught cold by the lively visitors and fell behind after just three minutes when some woeful defending gave striker Jack Lester the chance to fire home from eight yards.
Chesterfield hot-shot Jamie Ward fired wide soon after when he escaped Matt Clarke's clumsy challenge, but visiting centre-half Aaron Downes came to their rescue with a last-ditch tackle on Bradford winger Omar Daley.
The stunned home fans were reeling again in the 23rd minute when the impressive Darren Currie made it 2-0 with a sensational left-foot strike from the corner of the City box.
Bradford's new-look midfield took time to settle, but they finally got back into the game after 29 minutes when skipper Graeme Lee drilled a fierce right-foot free-kick beyond Trevor Carson from 19 yards out.
An amazing turnaround was completed nine minutes before the break when striker Michael Boulding powered home a free header from eight yards to level the scores and Boulding was unlucky not to double his tally with a neat flick at the start of the second period.
The hard-working striker should have done better when Conlon sent him clear soon after but he could only drag his shot wide.
As both sides pressed for the win in an end-to-end second period Lester wasted a great chance when he fired into the side-netting, but the visitors' hopes were dashed when Alan Goodall upended Nicky Law as he surged into the box.
The Chesterfield midfielder could have no complaints about his red card for a second bookable offence and Conlon kept his cool to chip in the penalty and put City ahead for the first time.
Substitute striker Peter Thorne almost put the icing on the cake when he diverted Conlon's pass into the net, but his neat finish was ruled out for offside.
In the final seconds Lester almost snatched an equaliser for the ten-man visitors but his shot flew over the bar.