Tyler Smith was City's hero as the Bantams secured a last-gasp 2-1 victory at Barrow to keep their play-off hopes alive.
City went into the break with the lead after Bobby Pointon smashed an effort past Paul Farman, but Barrow came back in the second half, equalising through a Kian Spence free-kick.
But substitute Tyler Smith stepped up in the dying seconds and kept the dreams of the City faithful alive with his 90th-minute winner.
City started the brighter in a dominant first half, and had the first decent chances of the game back-to-back in the 20th minute.
A point-blank save from Paul Farman after pinball in the box was eventually cleared for another corner, from which City were able to recycle the ball back into the box, where Andy Cook's header was held.
City were the side in the ascendency, and kept coming forward. Calum Kavanagh saw a shot flash wide just five minutes later - the Bantams' best opening at that time.
Graham Alexander's side made their strong start count just before the half-hour, as Bobby Pointon opened the scoring emphatically in the 27th minute.
Barrow could not clear their lines after a corner and the ball fell to Pointon, who took a touch and rifled a left-footed effort past Farman from just inside the area.
The hosts started the second 45 on top, looking for a response. Cole Stockton saw an effort cleared off the line just five minutes into the half, with Ciarán Kelly City's hero.
They could not hold out for much longer, however, and Barrow would equalise directly from a free-kick.
Kian Spence smashed an effort through the City wall, taking a deflection on its way through, and deceiving Sam Walker, to make it 1-1 just before the hour mark.
City knew they had to find a winner to take the play-off race to the final day, and threw bodies forward in their search for a second goal. The game plummeted into an end-to-end affair, with both teams pushing for the win.
Late on, Harry Chapman found space down the right-hand side and delivered a dangerous ball into the box, but it alluded Tyler Smith.
As the clock ticked into the 90th minute however, City found the goal that they were craving, and Tyler Smith put the away side back in front!
Cook played a lovely through ball into the box and Smith raced onto it, keeping his cool and bending his effort into the bottom corner to cue bedlam in the away end.
City defended resolutely as the game ran into nine minutes of additional time, to see out the victory and ensure they remain in with a chance of making the Sky Bet League Two Play-Offs, heading into Saturday's visit of Newport County.
BARROW: Paul Farman, Dean Campbell (Ben Whitfield 77’), Niall Canavan (C), Kian Spence, Elliot Newby, Robbie Gotts, James Chester, Luca Stephenson (David Worrall 77’), Emile Acquah (Dom Telford 82’), Cole Stockton (Jamie Procter 77’), Rory Feely. SUBS NOT USED: Josh Lillis, Sam Foley.
GOALS: Spence (59’).
CITY: Sam Walker, Brad Halliday, Matty Platt, Richie Smallwood (C), Calum Kavanagh (Harry Chapman 82’ (Lewis Richards 90+4’)), Andy Cook, Alex Gilliead (Clarke Oduor 77’), Ciarán Kelly, Daniel Oyegoke, Bobby Pointon (Tyler Smith 82’ (Jonathan Tomkinson 90+4’)), Tyriek Wright. SUBS NOT USED: Colin Doyle, Liam Ridehalgh.
GOALS: Pointon (29’), Smith (90’).
ATTENDANCE: 4,527 (with 624 visiting City supporters).
