United moved another step closer to the play-offs with a point in Saturday's Yorkshire derby.
Jason Holt's goal gave United the initiative but a strike in the last ten minutes from former Blads loanee Billy Clarke ensured the spoils were shared.
It was manager Nigel Clough's 100th goal in charge of the Blades and Jamie Murphy's 100 start, the Scotsman having a hand in Holt's second half goal.
Kennedy, Baxter and Murphy all started as Clough made three changes after the midweek defeat. Flynn missed out through injury, whilst Scougall and Done reverted to the bench. The Bradford teamsheet included no less than five former Blades.
Baxter began on the right, with Murphy on the left, but it was Bradford who were the quicker out of the blocks. From McMahon's pass, Halliday shot wide in the first minute, whilst Knott curled across goal soon after.
Despite a nervy start, United had a good chance to open the scoring on nine minutes when Davies caused problems for both the visiting central defenders from Brayford's cross but Murphy wasn't able convert the loose ball.
Bradford offered the bigger attacking threat in the opening 20 minutes but the action was thick and fast. Basham and Brayford did just enough to prevent Hanson getting a clean shot at Howard and then Basham cleared off the line from Clarke after Knott's shot dropped perfectly for the ex-Blades loanee.
At the other end, from Baxter's cross, Davies again caused problems with his presence which saw the ball drop for Coutts but his goalbound effort was blocked. Knott's run and shot was deflected wide as Bradford went back on the attack, but United began to see more of the ball as the half wore on.
The Blades were the better side late in the half. From Brayford's run, Davies turned his man but shot at the visiting goalkeeper and the striker also fired a free-kick into a Bradford wall. The last action saw Doyle the first in the referee's book, despite Knott, the man he supposedly fouled, protesting in the United skipper's favour!
Alcock replaced Kennedy at half-time, prompting a reshuffle of the defence, and Bradford had the first chance but Halliday was off target from Knott's cross. The Blades, however, managed to get a grip on the game and forced the visitors back.
A good move involving Coutts and Alcock saw Baxter's shot blocked by Meredith and, with 52 minutes gone, Davies struck a post with a header but he was adjudged offside.
United did, though, grab the lead on 57 minutes, with Doyle heavily involved in the build-up. The skipper set Murphy free on the right and then progressed to the box to challenge for the Scotsman's cross, causing enough of a nuisance for the ball to drop invitingly for HOLT to net at the Kop end.
The goal prompted Bradford into more attack-minded moves. Yeates, on as a substitute, had two efforts, including a powerful volley, but his first was saved by Howard and the second headed away by Brayford.
Adams replaced Baxter with around ten minutes to go but Bradford levelled soon after, with a couple of former Blades involved. A long free-kick saw Andrew Davies nod down and CLARKE pick his position in the bottom left corner of Howard's net.
The later moments saw United back on the attack, with Adams attempting to use his pace from the left. As the watch ticked around to 90 minutes, McArdle was sent off for a second bookable offence, blocking off Davies.
Five minutes of added time saw the Blades dominate but another chance was not forthcoming as Nigel Clough's side had to settle for a point.
Blades: Howard, Brayford, Basham, Doyle, Murphy, Baxter (Adams 81), Coutts, Freeman, Kennedy (Alcock 45), S. Davies, Holt.
Unused: Scougall, McNulty, Willis, Done, B. Davies.
Bradford: Williams, Darby, Meredith, A. Davies, Hanson, Clarke, Knott (Stead 83), Routis, McArdle, Halliday (Yeates 61, MacKenzie 90), McMahon.
Unused: Dolan, Liddle, Zoko, Urwin.