Chris Armstrong's second goal in a week enabled United to stretch the unbeaten away run to five games.
The converted midfielder's deflected header from James Beattie's superb cross was enough to beat Coventry City at the Ricoh Arena and lift the Blades to 11th in the table.
Armstrong's goal also completed a hat-trick of firsts for the Blades. Bryan Robson has now masterminded first victories for the club at three of the Championship's newest grounds following wins at the Walkers and Britannia Stadiums.
The midweek victory at Charlton enabled Robson to name the same squad for the visit to the Ricoh Arena, where Coventry were missing their top goalscorer Mifsud. The Maltese striker, a reported former United target, sat out the final match of three game suspension.
United enjoyed a lot of early possession, although the neat little passes failed to open up the home side, whilst all that Coventry could muster in the opening minutes were a cross and corner from Cairo but Kenny was untroubled.
United's first chance was a result of Gillespie finding space on the right. From his cross, Beattie won the header but although the effort looked off target, McNamee added a touch to clear for a corner.
Right-back McNamee raced on to a through ball, beating Naysmith, but lost the ball to Kenny as Coventry threatened but United hit back and de Zeeuw needed to be alert to keep the ball from Beattie and then Carney found Armstrong's run and although the resulting shot was not well-timed, Konstantopoulous almost made a mess of his save.
Twice Cairo went close but his first effort fell to his weaker left foot and then, with 32 minutes gone, he turned and struck a half-volley which Kenny needed to push over.
Later in the half the two goalkeepers were forced to work harder. On 37 minutes, Kilgallon spotted Tonge's run and after beating the offside trap the midfielder's shot was destined for the outside of the goalkeeper's right post before Konstantopoulous added a touch.
The home goalkeeper saved again seconds later, this time dropping to his left to keep out Beattie after Cahill had deliberately stepped over Gillespie's cross and then it was Kenny's turn, rushing across his goal to push away a Doyle effort after Gray's back-post cross.
The last effort of the half, including the one-added minute, was following a slip by Cahill. It gave Adebola the room to operate but the big striker fired across goal and wide with the United goalkeeper looking calm and aware that the effort was off target.
The first talking point of the second half was a booking - the game's first - for Bardsley, who prevented Gray progressing in to the box with a late challenge, whilst another collision moments later saw Konstantopoulous needed treatment after an aerial battle with Beattie.
Despite a slow start to the second period, the action began just before the hour when an inswinging free-kick from Gillespie saw an unmarked Beattie flick a header wide as Coventry appealed for offside.
Bardsley put his body on the line to prevent Adebola connecting with Cairo's cross then, in a similar move to the previous Blades attack, Gillespie swung in and Beattie this time forced Konstantopoulous to tip over.
The Greek goalkeeper could do little to prevent United taking the lead on 62 minutes. Carney came inside from his left flank, held on to possession, and fed the ball out to the right where Beattie went beyond Borrowdale before delivering a perfectly-flighted cross for ARMSTRONG to score with a header. A deflection off de Zeeuw may have taken the ball out of Konstantopoulous' reach. Regardless, Armstrong and Beattie celebrated in front of the Blades fans.
Moments later Tonge looked to extend the lead but his shot, after Beattie held the ball up, was deflected wide, whilst maybe Doyle's poor shot wide prompted Coventry boss Dowie to play more direct and bring on McKenzie.
Gillespie preempted a Tonge crossfield ball and got around the back of Turner but his shot only found the sidenetting, whilst, predictably, Coventry became more anxious and attempted to force United back.
Naysmith and Kilgallon made vital interceptions to keep out the home side and then Andrews struck a powerful shot from an acute angle but he was off target.
United were happy to run down the clock - Webber replaced Carney on the left - whilst the home side offered little. As the clock ticked around to 90 minutes, Osbourne won a corner but Cahill powerfully headed clear, and the Blades comfortably repelled the home side for the three minutes of injury-time to enable more than 2,000 Unitedites to leave the Ricoh Arena happy.
Coventry: Konstantopoulous, de Zeeuw, S. Hughes, Doyle, Adebola, Cairo (McKenzie 65), McNamee (Osbourne 45), Tabb, Gray, Borrowdale (Andrews 80), Turner.
Unused: Marshall, Ward.
Blades: Kenny, Naysmith, Bardsley, Beattie, Carney (Webber 84), Kilgallon, Montgomery, Tonge, Gillespie, Armstrong, Cahill.
Unused: Bromby, Stead, Gerrard, S. Quinn.
