An injury-time goal from Forest Green Rovers skipper Joseph Mills condemned the Bantams to their first league defeat of the season.
With the game seemingly heading for a goalless conclusion, Mills pounced to head home in the third minute of an extended period of overtime at the end of the match to clinch a 1-0 win for the visitors.
Incredibly, City thought they had equalised in the twelfth minute of injury time when Kelvin Mellor converted from close range, but the goal was ruled out for offside.
Attacking to The Kop in the first period, City began the encounter at a sun-drenched Valley Parade on the front foot.
Connor Wood, playing left back for the Bantams, curled over from outside the box after 13 minutes, while Anthony O'Connor and James Vaughan threatened from headers later on.
Following a water break 25 minutes in due to the warm temperatures, Forest Green's possession-based football slowly started to give the visitors' some joy.
Rovers captain Mills curled onto the roof of the net from a free-kick outside the box just after the half hour mark.
Another opening from Forest Green saw Kevin Dawson drag a low strike wide from the edge of the box.
As the half drew to a close, Jordan Gibson, who had earlier seen a decent penalty shout turned down, whistled a drive from distance narrowly past the far post.
The final act of a tight and keenly-contested opening period saw Mills' driven strike direct from a free-kick well held by a watchful Richard O'Donnell.
Sparked by the presence of Jamie Devitt off the bench for the second period, City began brightly after the restart, with Gibson firing wide via a low drive from outside the box.
Wood was required to be on high alert, however, minutes later when the defender made a superb last-ditch tackle to deny Dayle Grubb a clear run on City's goal in the box.
Grubb threatened again just past the hour point when he fired O'Donnell from edge of the box.
Despite Forest Green enjoyed strong periods of possession after the interval though, it was City who created the better scoring chances in the latter stages of the match.
From a Mellor long throw-in into the box, Ben Richards-Everton's headed flick on found Devitt, but the sub midfielder's shot was pushed away by 'keeper Joe Wollacott
As the game entered the final ten minutes of normal time, City created arguably their best opening of the match.
Devitt's lofted free-kick into the box eventually dropped at the feet of Clayton Donaldson , but the striker's powerfully-struck close range effort was somehow cleared off the line.
Seconds later, Gary Bowyer's men threatened again as they kept the pressure on, but Vaughan's header was blocked away from right in front of goal by Matt Mills.
Although eight minutes of injury time were originally signalled, the game seem set to be drifting to a drawn fixture until Joseph Mills pounced to head in from close range.
The drama was over yet, though, with Matt Mills given his marching orders for a second bookable offence in the last of those scheduled eight minutes.
That delay meant the game crept on a little longer, with City given one last chance from a corner.
Woods' delivery into the box was headed on by Richards-Everton, Mellor converted from just yards out but his celebrations were sadly cut short by the linesman's flag.
CITY: Richard O'Donnell; Kelvin Mellor, Anthony O'Connor, Ben Richards-Everton, Connor Wood; Hope Akpan, Daniel Devine (Jamie Devitt 46'), Matthew Palmer (Callum Cooke 74'); Jordan Gibson (Sean Scannell 65'), Clayton Donaldson, James Vaughan (c) Subs not used: Sam Hornby, Paudie O'Connor, Jermaine Anderson, Omari Patrick.
GOALS: None.
CAUTIONS: Devine (22'), Donaldson (36'), Vaughan (80'), Akpan (85'), Richards-Everton (90+11).
FOREST GREEN ROVERS: Joe Wollacott; Farrend Rawson, Matt Mills, Udoka Godwin-Malife (Dominic Bernard 54'), Liam Kitching (Nathan McGinley 68'); Carl Winchester, Ebou Adams, Kevin Dawson; Joseph Mills (c), Shawn McCoulsky (Matthew Stevens 79'), Dayle Grubb Subs not used: Lewis Thomas, Aaron Collins, James Morton, Junior Mondal.
GOALS: J Mills (90+3).
CAUTIONS: Adams (40'), Kitching (58'), Winchester (77'), (M Mills 84'), Grubb (89').
DISMISSALS: M Mills (90+8)
ATTENDANCE: 13,504 (121 visitors)
REFEREE: Andy Haines