United chalked up an impressive victory on the road in Saturday's Yorkshire derby.
In front of the Sky cameras, the Blades netted twice in the second half to beat ten-men Bradford City.
Bob Harris scored his first Blades goal and Marc McNulty added a late second to seal the win.
United made two changes from the draw with Leyton Orient. Basham and Campbell-Ryce returned, Flynn dropped to the bench and Wallace was a notable omission, although he did limp out of the previous fixture. Bradford's squad of 18 included no less than four players who have represented the Blades - Davies, Yeates, Clarke and Stead.
Bradford were the quicker out of the blocks but all they had to show for it was an early 25-yard free-kick from Sheehan, which was a yard wide. After weathering the initial onslaught, United hit back with a few decent chances.
Basham robbed Routis, which allowed Baxter to set up Murphy but his weak shot was saved by the home goalkeeper. Moments later Pickford saved from Murphy again, this time after Campbell-Ryce had beat Sheehan and Yeates on the right.
Either side of McEveley leaving the field, injured, and being replaced by McGahey, Baxter had two opportunities. His first was blocked by the head Davies and his second, on 26 minutes, was saved after good work from Murphy.
Sheehan's corner caused mayhem in the Blades box but the visitors survived with Hanson fouling Basham and a 25-yard free-kick from Yeates was deflected over.
As half-time approached, Basham played in Baxter but again Pickford saved and the last action before the break was Campbell-Ryce picking up a booking for a foul near halfway.
Just 13 seconds into the second period the drama began. Bradford had yet to touch the ball when Murphy let the ball run through the legs of Darby, who dragged back the Scotsman. It was cynical and Darby was already on a booking so when referee Hooper whipped out his yellow card it was quickly followed by a red.
Davies did well to prevent Basham getting a clean header at goal following a quick corner and Murphy cut inside and almost found Baxter in space as Bradford looked to come to terms with playing with ten men.
On 61 minutes, Murphy cut in from the left and fired into the sidenetting but he played a part in United taking the lead soon after. Campbell-Ryce's deep cross was not dealt with by replacement right-back Routis and Murphy laid off to HARRIS, who curled away from the goalkeeper, perfectly into the corner of the net from 20 yards.
Bradford survived a major penalty shout when Scougall was literally wrestled to the floor and then Basham was booked for kicking the ball away. Hanson won a header from a corner but Howard was well placed and the Blades goalkeeper then produced probably his best save of the season on 77 minutes. McGahey conceded a free-kick on the edge of the box and Sheehan's powerful free-kick looked like it went through the wall but Howard kept an eye on the ball and pushed away to safety.
McNulty replaced Scougall and it was to prove influential but only after an unmarked Kennedy hit a post with a header from six yards and then saw another headed clear by Baxter. Then came the sealer. Basham's through ball should have been cut out by Davies but he made a mess of his control, allowing McNULTY to attack Pickford's goal and score with confident finish.
In the closing minutes Bradford looked to add respectability to the scoreline but Howard pushed away a shot from Morais and a Yeates cross came off the crossbar.
Five minutes of added time was announced but Howard protected his clean sheet with another save from Morais and moments later the 1,997 Blades fans that made the trip were celebrating a deserved victory.
Bradford: Pickford, Darby, Davies, Sheehan, McLean (Morais 53), Hanson (Stead 74), Clarke (Knott 57), Yeates, Kennedy, Routis, McArdle.
Unused: Meredith, Dolan, Williams, Halliday.
Blades: Howard, Alcock, Harris, Basham, Doyle, Murphy, Scougall (McNulty 79), Baxter, McEveley (McGahey 22), Campbell-Ryce (Flynn 85), McCarthy.
Unused: Davies, Porter, Reed, Turner.