It was birthday boy Billy Clarke who grabbed the all-important goal just before the hour mark, celebrating turning 27 as he smashed home from almost 25 yards, leaving Bantams boss Phil Parkinson delighted.
He said: “Billy’s moment of pure quality has won a really tough game – it was fit to win any game. We were on the back foot a bit towards the end, but overall I felt we were worthy winners.
“We knew we’d be in for a difficult afternoon, but the sending-off didn’t help Chesterfield.
“The lad has flung his elbow into Andy’s face, though. It was a dangerous one.”
Jon Stead was in the thick of the action early on, heading inches over the top when he should have got his effort on target.
Armand Gnanduillet replied for the Spireites with a smart strike which flew narrowly wide, but the score remained goalless.
The Spireites were reduced to 10 men three minutes after the restart when referee Eddie Ilderton sent Sam Morsy straight off after connecting with Andy Halliday with a flailing arm.
The Bantams took full advantage in the 57th minute, with Clarke crashing home superbly from just outside the box.
The hosts pushed hard for an equaliser late in the game, but Bantams’ goalkeeper Jordan Pickford was the hero on a couple of occasions, most notably when superbly keeping out Jay O’Shea’s well-struck drive.
Chesterfield: Lee, Darikwa (Boco 83), Raglan, Clucas, Margreitter, O’Shea (Gardner 84), Ryan, Roberts (Ariyibi 88), Morsy, Doyle, Gnanduillet. Unused substitutes: Hird, Humphreys, Evatt, Wright.
Bradford City: Pickford, Darby, Davies, Meredith, McArdle, Clarke (Zoko 90), Morais, Liddle, Halliday (Knott 62), Yeates, Stead (Hanson 84). Unused substitutes: Sheehan, Williams, Kennedy, Routis.
Referee: Eddie Ilderton (Tyne & Wear).
Man of the match: Jordan Pickford.