Bladeacoaster - the phrase coined by Nigel Adkins this week - could be used to describe this Yorkshire derby.
United went 2-0 but fought back with a Chris Basham-pressured own goal and a Billy Sharp equaliser.
In an entertaining fixture, both sides had chances to win it in injury-time with Jose Baxter clearing off the line with the last touch of the game.
Reed and McNulty started as boss Adkins made two changes, the duo replaced Baxter and Sammon, who dropped to the bench. Bradford included two former Blades, McMahon and Davies, amongst their substitutes.
United won two corners in the first minute but, expectedly, Bradford's aerial prowess came to the fore early on, winning a number of free-kicks in the Blades half and a couple of corners. There was also a penalty appeal when McEveley and McArdle clashed, whilst the United skipper was booked for his second foul on Marshall. Additionally, also in the first 15 minutes, Edgar was forced to clear over his own crossbar and Howard kept out an inswinging free-kick from Evans and a header from Hanson.
There was a spell of calm after the initial onslaught and United saw more of the ball as the half hour mark approached. A move involving Reed, Sharp, Campbell-Ryce and McEveley saw McNulty's header held under the crossbar by Jones and then Sharp put the ball in the net on 28 minutes but he was adjudged to have been offside when converting McNulty's pass.
Bradford, however, nicked the advantage on 33 minutes. From Anderson's cross, Edgar and Cole challenged and from the loose ball, MEREDITH beat Howard in a foot race before clipping over the goalkeeper.
The home side went close again when Evans shot from 25 yards but it was directly at Howard and the half ended with the Blades trying to get back on top but goalkeeper Jones was not called into action.
United made a change at the break, Alcock introduced for McEveley, with Freeman switching to left-back, but there was more disorder to follow. Liddle's clip down the left channel saw the ball bounce and Edgar's attempted clearance hit COLE and flew past Howard.
A couple of corners and a Reed shot saw United look to get back into the game, whilst Adkins brought on Baxter and Sammon just before the hour, making it a front three.
Collins headed over Baxter's corner but the lifeline was just minutes away. Alcock's long throw saw Basham and Meredith challenge, with the ball looping over Jones and into the far corner of the net. Basham celebrated but the goal was credited as a MEREDITH own goal.
Sammon fired over the top and Bradford appealed for another penalty when Anderson's cross hit Alcock but referee Swarbrick was unimpressed and moments later United's equaliser arrived.
On 70 minutes, Baxter's flighted ball saw SHARP get around the back of the defence and although his first effort was blocked, he showed great composure and balance to poke home the rebound.
The action continued for the near 20,000 crowd and thousands watching on TV. Anderson's flicked header was held by Howard and Marshall curled wide. For United, from a break, Sammon played in McNulty but he sliced wide.
The last ten minutes were nervy for both sides but the Blades were on top, whilst five minutes were added as injury-time. Just in the additional period, Baxter's inswinging free-kick saw Collins denied by an impressive Jones save, whilst the very last touch was an important once. Bradford swung in a free-kick and a corner and from the latter Hanson's header was goalbound but Baxter cleared off the line.
Bradford: Jones, Darby, Meredith, Evans (Knott 79), Marshall (James 90), Liddle, Hanson, Burke, McArdle, Anderson, Cole (Davies 79).
Unused: Williams, Clarke, Leigh, McMahon.
Blades: Howard, Freeman, Basham, Sharp, McNulty, Collins, Woolford (Baxter 59), McEveley (Alcock 45), Campbell-Ryce (Sammon 59), Reed, Edgar.
Unused: Scougall, Higdon, Long, McGahey.