A deflected first half strike from home midfielder Antoni Sarcevic was ultimately the difference as the Bantams were edged out of a tight encounter with Plymouth Argyle.
In a game of few clear cut chances, Plymouth claimed all three points when Sarcevic swooped to fire home just over ten minutes from the break.
The goal had more than a touch of fortunate about it, though, with Sarcevic's drive past Colin Doyle from inside the box taking an important deflection off Nathaniel Knight-Percival on its way into the net.
After a fairly conservative approach in the first period, City pushed for an equaliser after the break, with sub Tyrell Robinson threatening during one opening after Alex Gilliead had fired dangerously across the box.
Simon Grayson's men sadly finished the game with ten men when Charlie Wyke was given his marching orders for a stray arm against Sonny Bradley in the final minute of normal time.
Plymouth came into the game on the back of an impressive five-game winning streak, but there was no real signs of any early alarms for the Bantams against their in-form opponents.
Playmakers Graham Carey and Ruben Lameiras tried to get on the ball for the hosts and pull the strings when they could.
On the whole, however, Grayson's well-drilled troops managed to keep their threat under wraps.
Lameiras - the Portuguese former Coventry City attacker - did warm the hands of Colin Doyle with a sixth-minute shot, but Paul Taylor responded with a similar effort for City at the other end soon after.
Taylor then troubled Plymouth shot-stopper Remi Matthews again later in the half with a shot on the turn from just inside the box.
In truth, there was little in the half as proceedings moved past the half hour mark.
As sometimes happens when confidence levels are up, however, a slice of luck went in favour of Plymouth to move them into the lead.
Lameiras' pass into the box found the well-timed run of Sarcevic to give the midfielder a sight of goal.
Sarcevic's goal-bound shot looked to be heading into Doyle's save range, but a crucial touch off the body of Knight-Percival saw the effort loop up over the diving frame of the City 'keeper and into the net.
Understandably, Plymouth's tails were up at this stage following Sarcevic's opener, and they pushed for a second before the break.
Lameiras fired narrowly wide of the near post with a drive from inside the box after Graham Carey had crossed low into the middle.
Carey himself went close towards the start of the second half when he fizzed a rising drive just past the side-netting by Doyle's near post.
Grayson responded by bringing on Robinson and Dominic Poleon just before the hour point, and the changes seemed to have the desired effect.
City were able to play further into Plymouth's half with greater regularity and give the hosts more to worry about.
The Bantams still needed to keep things locked up at the back, however, and Romain Vincelot was required to make a brave block after Bradley had headed Lameiras' far post corner down into the path of Sarcevic.
The strong piece of defending from City's skipper would prove to be his final meaningful act of the game, with the Frenchman making way for Matthew Lund soon after in the Bantams' final substitution of the day.
As City looked to make it a nervous ending for the hosts and their fans, they created arguably their best chance of the afternoon just over ten minutes before the end of normal time.
Gilliead played a low cross into the middle, Robinson, looking for a repeat of his recent Charlton Athletic goal, again got across his full back from the other flank but this time the winger couldn't get a proper touch on the ball as it agonisingly fizzed across the box.
Any decent touch from the winger there would have surely given City a great chance of getting back on level terms.
In defence of Robinson, though, the youngster did claim a push in the back by his marker Oscar Threlkeld that went unspotted.
The Pilgrims brought on defensive duo Yann Songo'o and Aaron Taylor-Sinclair in the closing stages as they looked to see out the game.
City's chances of creating an uncomfortable finish to the game for Plymouth were dealt a blow by a red card to Wyke just before injury time.
After consulting the assistant referee nearby, referee Mr Graham Salisbury gave Wyke a straight red card for his tangle with Bradley.
It remains to be seen if City will appeal the red card, although the striker was protesting his innocence post-match.
With City now a man light but still pushing forward for a late leveller, Plymouth could have netted a second in the fouth and final minute of injury time.
City were caught out playing out from the back, Jamie Ness tackling Callum Guy to give himself a clear sight of goal.
Ness only had Doyle to beat but the midfielder's lofted effort past the 'keeper from an angle drifted just past the far post.