Rabbi Matondo finished off a brilliant counter-attack to register for the Blues, but that wasn’t enough to cancel out Adam Thompson and Alex Jones’ first half strikes.
A superb reflex save from Aro Muric was the first action of note as he displayed cat-like reactions to deny Shay McCartan from close range in the third minute.
The forward may have called the City custodian into action again moments later as he capitalised on Ed Francis’ slip. McCartan looked set to race clear but the defender made a recovery, albeit one that earned him a place in the referee’s notebook.
After that highly charged opening the game settled as both sides tried to work each other out – both lacking a cutting edge when they probed in attack.
But Bradford forced a breakthrough via an 18th minute corner.
The imposing figure of centre-half Thompson leapt highest and met the lively Tyrell Robinson’s centre with a powerful header which gave Muric no chance.
City hit back immediately through Benjamin Garre, who’s footwork was eye-catching throughout.
The Argentine forced his way to the by-line and flashed a low ball across goal, but there was no-one to meet it and Tom Dele-Bashiru fired over when the resulting clearance fell to him 20 yards from goal.
The Blues’ best chance of the opening period fell to Matondo after an inch-perfect ball over the top from Matt Smith, but the winger's near-post effort was comfortably saved.
Ten minutes before the half the Bantams doubled their lead as Jones turned smartly in the six yard box and fired into the bottom right corner.
A fantastic save from Muric ensured the second period started in a similar vain to the first.
Unmarked on the left of the area, Jones' low effort looked destined for the bottom corner, but the 18-year-old was equal to it and turned it away for a corner at full-stretch.
City rallied and pulled one back with a fine counter-attack just before the hour.
Dropping deep, Lorenzo Gonzalez set the onrushing Matondo clear of the defence and he coolly rounded the keeper to give himself the simplest of tap-ins.
The Welshman was involved again shortly after as he produced a performance that belied his tender years.
Haring down the right he delivered a teasing ball that reached Garre at the far post but he didn’t connect cleanly and it was a comfortable save for Lukas Raeder.
It was a much-improved performance from the young Blues, who carried more of an attacking threat in the second half and reduced Bradford to half chances as the defence remained resolute.
Yet, the same could be said for the home side, who repelled several City attacks following Matondo’s strike to see out the game.
The manager made four changes to the team that started against Rotherham in August and was without the injured Brahim Diaz as well as Phil Foden and Joel Latibeaudiere, who are at the World Cup with England U17s.
Muric retained his spot in goal, with Duhaney, Oliver, Francis and Wilson in front of him.
Smith captained the side for the first time and he was alongside Dele-Bashiru.
Ahead of them were Matondo, Richards and Garre, who formed a trio behind Gonzalez.
The EDS travel to West Ham United in the Premier League 2 on Saturday afternoon as they look to build on their win against Derby County and register back to back victories in the league for the first time this season.
What it means
The result leaves City third in Group F. Four points behind Bradford, who top the group and level with Chesterfield, who edge them out of second place on goal difference.
Davies' side travel to the Proact Stadium in late November for the final group stage game, known an outright win, or via penalties, will be enough to see them through to the next round.