This Yorkshire derby lived up to its pre-match billing and a point each was well deserved in an action-packed game.
Billy Sharp twice put the Blades ahead but it took a Chris Basham leveller to share the spoils.
A sell-out away end of 2,716 applauded the efforts of Chris Wilder's team at the final whistle.
For the encounter, boss Wilder named an unchanged team following the midweek victory over Shrewsbury Town. O'Connell, back from illness, took Whiteman's place on the bench. Bradford's starting XI included three ex-Blades - Law, Clarke and Kilgallon.
As expected, there was a lively start, although a lack of chances early on. Clarke should have done better from a Law cross before United took the lead on 18 minutes.
Lafferty and Wright did well to win possession in Bradford's half before Duffy floated a ball over Vincelot's head for SHARP to expertly nod into the top corner, beating Doyle, who appeared well-placed.
United went close to a second moments later, from a Coutts corner, the home 'keeper failed to collect and Lafferty's shot was wide, although he argued his effort had been deflected.
Basham and Duffy picked up bookings but again United went close. Another teasing cross from Duffy saw Done pull to the back post but he could not get enough purchase to beat Doyle.
The game was very open, maybe too much so for Wilder's liking, and Bradford levelled on 35 minutes. Kilgallon's low cross from the left eluded a crowded six-yard box and found its way to CLARKE, who touched home at the back post.
The final ten minutes of the entertaining period were also end-to-end, but with a lack of clear chances, although Done picked up United's third booking.
Two minutes into the second half United had the ball in the net but Sharp was adjudged to have fouled Dieng from Duffy's quick free-kick. Sharp also fired over after Done was a pest but the leading scorer and skipper was not to be denied a second goal.
On 51 minutes, a free-kick wide on the left saw Fleck catch out the whole home defence and SHARP was left unmarked to beat Doyle from close range.
Bradford hit back. Cullen's shot was pushed around the post by Moore, although the referee gave a goal-kick, but the home side levelled again around the hour mark. A cross from the right was mis-kicked by Hanson but the ball dropped perfectly for HIWULA to touch in at the back post.
The action was frantic and Wilder added Basham to the midfield in an offensive move. Sharp turned inside from the left but was denied a hat-trick by Doyle pushing his shot away and then Bradford took the lead for the first time. Kilgallon's cross from left was turned in by DIENG.
Wilder made a double change, introducing Scougall and Lavery, and within minutes the Blades were level. A Fleck corner saw Hanson miss his kick and BASHAM ran away to celebrate after the ball was touched in, via the back post.
With 15 minutes to go a forward ball saw Lavery put the home defence under pressure but again Doyle saved from Sharp. At the other end, late on, a break saw Hiwula head against the crossbar following Law's cross. Moore may have added a vital touch.
The final moments were tense. Duffy shot at Doyle and four minutes of added time began with a Bradford corner. The home side also won a free-kick in a dangerous position late on but United defended well and protected a valuable point.
Bradford: Doyle, Law, Vincelot, Dieng, Hanson, B. Clarke, Hiwula, Cullen, Knight-Percival, McArdle, Kilgallon.
Unused: Darby, N. Carke, Marshall, Sattelmaier, Vuckic, Morais, Devine.
Blades: Moore, Fleck, Basham, Sharp, Done (Scougall 70), Wright, Coutts (Lavery 70), Freeman, Ebanks-Landell, Duffy, Lafferty.
Unused: Hussey, O'Connell, Brown, Ramsdale, Chapman.