Mark Hughes' Bantams fell to their first defeat in six games, narrowly losing 1-0 to Barrow at the University of Bradford Stadium.
Joshua Kay scored the game's only goal for the visitors just before the half-hour mark, giving Pete Wild's side the lead, and ultimately, the three points.
After a sustained amount of possession, it was City who started the stronger, as Alex Gillead's long-range effort was charged down by Thomas White.
Seconds later, Adam Clayton's inviting through ball fell to Andy Cook, but City's No.9 was flagged offside.
Despite the promising opening for the hosts, it was the visitors who struck first through Kay.
After Barrow won the ball back inside City's half, it was played to the Bluebirds’ No.11 by Ged Garner who gave the away side the lead from 12 yards out.
The visitors ended the half strongly after a curled effort from Elliot Newby drifted past Harry Lewis' goal as they went into the interval with their lead intact.
The Cumbrian outfit started the second half as they ended the first, as Niall Canavan almost added to their lead, moments before Robbie Gotts' 20-yard effort flew straight at City's No.1.
Just after the hour mark, Hughes' side continued to search for an equaliser and came close from a Gilliead shot just inside the box, but his effort was deflected wide for a corner.
Heading into the final 10 minutes of the game, the Bantams' search for a goal intensified, and they came close from a corner - where Sam Stubbs' headed effort looped over the bar.
Despite City's late efforts, the Bluebirds' travelled back to Cumbria with all three points.
CITY: Harry Lewis (GK), Brad Halliday (Scott Banks 59'), Liam Ridehalgh, Matty Platt, Richie Smallwood (C, booked 38', Vadaine Oliver 80'), Andy Cook, Jamie Walker (booked 36'), Alex Gillead, Abo Eisa (Dara Costelloe 45'), Sam Stubbs, Adam Clayton. Subs not used: Colin Doyle (GK), Ryan East, Harry Chapman, Ciarán Kelly.
BARROW: Paul Farman (GK), Patrick Brough, Sam McClelland, Niall Canavan (C), Elliot Newby, Joshua Kay (Benjamin Whitfield 81'), Thomas White, Harrison Neal, Robbie Gotts (Sam Foley 70', booked 93'), Ged Garner (Billy Waters 73'), George Ray. Subs not used: Josh Lillis (GK), Tyrell Warren, Richard Bennett.
GOALS: Kay (25').
ATTENDANCE: 17,071 (511 Barrow supporters).