Late goals in each half saw the Blades succumb to defeat in the first Yorkshire derby of the season
The in-form Nahki Wells scored both the Bradford City goals, including a scuffed second.
United created plenty of chances and had Jamie Murphy netted in the third minute, David Weir may not have suffered a second consecutive away defeat.
Boss Weir named an unchanged team for the visit to West Yorkshire, although on the bench Flynn and Ironside took the places of Johns and Eyre. Bradford kicked off with the same XI that has started every game since they returned to League One.
Early indications were that Murphy was playing in a central role behind Taylor, with McFadzean and Brandy wide. United took just two minutes to open the home defence and it came from a Bradford corner - Taylor produced a defence-splitting pass to put Murphy clear but his shot was saved by the legs of goalkeeper McLaughlin.
Soon after McMahon's free-kick was on target but comfortable for the goalkeeper, whilst Bradford thought they had taken the lead on 15 minutes when Wells, who had already shot wide, was denied by a tremendous Long save following Meredith's pull back.
Twice in a matter of minutes, Brandy went close for the Blades. He stung the palms of McLaughlin after a neat flick from Taylor and then was denied by McHugh with penalty appeals waved away.
Murphy's run at the home defence ended with a shot at McLaughlin, whilst the Blades were twice indebted to Long in the space of minutes. The goalkeeper saved a powerful shot from Wells after Bradford benefitted from a deflection off the referee and then a 25-yard Yeates free-kick was pushed away by the teenager.
However, despite his efforts to keep the scoreline blank, Bradford took the lead on the stroke of half-time. McGinty was beaten in the air and WELLS took advantage, using quick feet to make space from Collins before drilling across Long and into the net.
The Blades made a change at the break with Flynn replacing McFadzean and boss Weir was forced into another, just moments into the second period when Brandy limped off holding his hamstring. Ironside was introduced and Taylor dropped into a more withdrawn position.
The second half did not begin at the same break-neck speed as the first but livened up around the hour mark. United won a couple of corners, which caused carnage in the penalty area, whilst Long was almost caught out by an uneven bounce.
Flynn's shot looped up after a significant deflection and McLaughlin was forced to tip over and the Blades had a great chance to level on 72 minutes but Ironside volleyed over after Flynn headed Coady's cross back into the danger area.
As the final 15 minutes approached, Maguire headed wide a free-kick from McMahon and Coady's long range shot was comfortable for McLaughlin but the Blades were applying the pressure and delivering plenty of crosses.
Maguire was the first booking, on 82 minutes, for a foul on Wells, whilst United's last change was Porter replacing McGinty. The Blades were throwing all resources into attack and were Doyle was forced to clear up an attack before Bradford added their second on 87 minutes. Long saved from De Vita but the rebound dropped to WELLS, whose mis-kick found the net.
Wells also went close with a late free-kick before the final whistle.
Bradford: McLaughlin, Darby, Meredith, Davies, Hanson, Thompson (De Vita 78), Yeates (Reid 65), Jones, Wells, McArdle, N. Doyle (Ravenhill 88).
Unused: Ripley, M. Taylor, McHugh, Connell.
Blades: Long, Maguire, M. Doyle, L. Taylor, Collins, Coady, Brandy (Ironside 50), McGinty (Porter 83), Murphy, McFadzean (Flynn 45), McMahon.
Unused: Howard, Westlake, Hill, McGinn.