United suffered a first league defeat in four games after a tough encounter at Swansea.
A tap-in midway through the second half was the difference between the teams.
Wilder named an unchanged starting XI and bench for the long trip and the early moments were interrupted by a head injury sustained by van der Hoorn following an aerial challenge with Egan.
United had a lot of early possession but there was only a long-range Fleck shot to show for the endeavour, which was comfortably saved by Mulder.
Baldock half-volleyed over after a corner and United's chances continued. On 21 minutes, Mulder made a tremendous save with his feet to deny Sharp following a Stevens cross.
Down United's left flank, Stevens and Fleck caused problems for the Swans, whose first serious effort resulted in Celina's dangerous delivery across the box being half-cleared before a Blades free-kick was awarded.
On 40 minutes, McGoldrick's flicked header flew wide from Duffy's cross and just before the interval Mulder saved Swansea again, this time keeping out a McGoldrick cross that deflected off substitute Carter-Vickers, a former Blade.
Also before the break, Celina was given space to attack United but his shot from outside the box faded well wide of Henderson's left post.
Swansea started the second well, though, and following a fortunate free-kick on the edge of the box, Grimes curled over Henderson's crossbar. The home side were seeing more of the ball and forcing the Blades back.
There was a warning shot when O'Connell poked the ball away from McBurnie, who was ready to pounce on Dyer's near-post cross but the two Swans combined well soon after to grab the lead. This time Dyer got around the back on the right and pulled back for McBURNIE to turn the ball past Henderson from close range.
Dowell was introduced but Swansea remained a threat. O'Connell blocked from Dyer and Henderson made a double save from Celina and James.
Madine was introduced for his debut to give United another attacking option but still the opportunities came from the home side. A fortunate touch from McBurnie opened up a chance for Naughton, whose effort was deflected wide and Celina's free-kick was also off target.
As the game entered the final ten minutes, Clarke was added to the attack and United put more pressure on the Swansea back line but goalkeeper Mulder was barely troubled.
Sharp went in on Mulder after a ball into the box and there was an unsuccessful appeal for an injury-time penalty when Sharp's attempted cross was blocked by van der Hoorn's arm. The resulting corner from Norwood found Clarke but dropped into Mulder's arms and it was the last action of a frustrating encounter.
Swansea: Mulder, van der Hoorn, Fer, McBurnie, Celina, Dyer (Fulton 81), Routledge (James 45), Grimes, Rodon (Carter-Vickers 21), Roberts, Naughton.
Unused: McKay, Baker-Richardson, Nordfeldt.
Blades: Henderson, Baldock, Stevens, Fleck (Madine 74), O'Connell, Basham, Sharp, Egan, Norwood, McGoldrick (Clarke 81), Duffy (Dowell 66).
Unused: Coutts, Stearman, Johnson, Moore.