Billy Sharp's 15th goal of the season was the difference as United got the better of Port Vale at Bramall Lane on Saturday.
Sharp netted early in the second-half in front of the Kop as the Blades came out on top in a hard fought clash against Rob Page's Valiants.
Boss Adkins made three changes from Tuesday's loss at Bury, with Sharp, Flynn and Woolford all recalled to the starting XI. Calvert-Lewin and Campbell-Ryce dropped to the bench, where they were joined by the returning Cuvelier.
There was a clear change in formation for United, who started with a 3-5-2 system. Basham, Edgar and McEveley were three centre-halves, with Brayford and Woolford playing in advanced wide roles. And it was the hosts who had the first shot in anger, with Neal saving from Adams who had been freed by Edgar's through ball. At the other end, Grant's shot was deflected wide for a corner.
United continued to be the ones forcing the issue, firstly, Duffy had to make a last ditch clearance from Brayford's centre, then the Blades right-back fired over from a promising position. In the 25th minute, for the second time the Blades had the ball in the back of the net, but after Hammond had been adjudged to have fouled Neal, Sharp was denied by the linesman flag.
As the game passed the half hour mark, Hammond became the first player into the book, for a challenge on McGivern. Hammond was then in the thick of the action again ten minutes later, only to see Dickinson head his goal bound header off the line, although again, the linesman had his flag raised. Following a quick break, Basham was booked for a mistimed tackle on Kennedy.
The last action of the first period saw Sharp fire wide under heavy pressure after Brayford and Flynn had seen efforts blocked.
Within five minutes of the restart, the Blades went in front and it was that man SHARP who fired home on the turn in front of the Kop after McGivern failed to deal with Hammond's cross from the right. One nearly became two moments later, Flynn released Adams, who held off McGivern before teeing up Sharp who shot inches wide.
Vale made two changes in quick succession, prior to McGivern side footing over when well positioned on the edge of the area. The subsequent break in play saw Cuvelier introduced for his first appearance of the season, replacing Hammond. Substitute Kelly then went into the book for a nasty lunge on Reed.
The game was an open affair, United looked threatening on the break, whilst Vale had a couple of speculative efforts from long range, prior to Adams receiving a standing ovation as he was replaced by Done with ten minutes remaining. The final change came moments after with Coutts taking the place of the hard working Flynn.
As the clock ticked down the visitors mounted a sustained period of pressure, but McGivern's foul and subsequent booking for a foul on Sharp took a bit of the sting out of the game, as the fourth official signalled there would be a minimum of four added minutes.
But despite Vale's best efforts and a number of balls into box, the Blades deservedly returned to winning ways at Bramall Lane.
Blades: Long, Brayford, Basham, Flynn(Coutts 82) Sharp, Woolford, McEveley, Reed, Adams (Done 80), Edgar, Hammond (Cuvelier 66).
Unused: Howard, Campbell-Ryce, Calvert-Lewin, McGahey.
Port Vale: Neal, Purkiss, Dickinson, McGivern, Duffy, Kennedy, Foley, Moore (Kelly 62), Leitch Smith (Dodds 75), Robinson (Hooper 57), Grant.
Unused: Streete, O'Connor, Brown, Boot.