Had he found the net, the Blades would have been welcoming West Bromwich Albion for Tuesday's massive Premier League game on the back of two morale-boosting results in Manchester, rather than one.
In this season of fine margins, for them, they were just the wrong side of another.
Up until then, the only real lapse had been to switch off for a few first-half seconds as a typical Manchester City pull-back came in from the right. It was all the top-of-the-table side needed, and they won 1-0.
It was, though, a defeat with honour, the Blades doing an otherwise sterling job defensively, and causing problems in the final minutes.
Aaron Ramsdale made three top drawer saves but, like his opposite number Ederson, he had an otherwise quiet afternoon.
Manchester City are a good enough side, especially on their own patch, that you really do not need to give them any gifts.
Having done that just nine minutes in, though, the Blades showed good spirit to stay in the game
It had been a fairly nondescript start to the game until good footwork by Ferran Torres saw him dance to the byline past Jayden Bogle, back in the side, and pull the ball back.
Gabriel Jesus's poor touch ought to have cost him the chance to score but he was in so much space that he was able to dig the ball out from under his feet and find the net, for the first Premier League goal by a Manchester City centre-forward since early November.
For a down-their-luck side against one flying at the moment, that could well have been the signal for the roof to come in. City had 75 per cent of the first-half possession, but very few chances to show for it.
Bernando Silva was given a glimmer in the 16th minute when he was almost able to run onto Oliver Norwood's header, but it just about found its way into the grateful arms of Ramsdale.
Jesus shot wide in the 22nd minute, but the chance was made much harder by the pressure he was put under by Chris Basham. The centre-back got an appreciative thumbs up from his manager.
Slowly, as the visitors began to realise their hosts were not hurting them, they got a little bit more careful in possession and began to take a few swings themselves.
Rhian Brewster's shot on the turn from Norwood's good pass into his feet lacked power, but at least Ederson had finally been worked, 36 minutes in.
When Oliver Burke charged the ball down five minutes before the break it took a good tackle from Ruben Dias to stop him going through on goal.
There was just as much hunger in defence, Norwood ending the half by throwing himself in front of an Aymeric Laporte shot that would have stung on a bitterly cold afternoon, as John Lundstram would from Oleksandr Zinchenko shortly after the break.
Torres started the half with a poor header from the left-back's cross, putting in beyond the far post, and Ramsdale came bravely out to Jesus's feet from a lovely Torres ball, but the hosts offered surprisingly little.
When Burke's cross was only half-cleared, Bogle sliced shot.
After 73 minutes Ramsdale flew right to deny Zinchenko, then tipped Laporte's header over from the corner.
Five minutes later, Wilder went for it. David McGoldrick had already been brought on and now Sharp and Oli McBurnie were too, to lead a 4-1-3-2 formation.
It led to Fleck's chance but it went begging, as did Jesus's when Ramsdale made a brilliant stoppage-time save from Jesus.
The Blades had lost, but only just.
Manchester City: Ederson; Walker, Dias, Laporte, Zinchenko; Fernandinho, Gundogan; Bernardo, Torres (Rodrigo 90), Foden; Jesus.
Unused substitutes: Steffen, Stones, Sterling, Mendy, Mahrez, Cancelo, Garcia, Bernabe.
Sheffield United: Ramsdale; Basham (Sharp 78), Egan, Ampadu; Baldock, Lundstram, Norwood, Fleck, Bogle; Brewster (McGoldrick 62), Burke (McBurnie 78).
Unused substitutes: Mousset, Lowe, Jagielka, Foderingham, Bryan, Gordon.
Referee: D Coote (Nottinghamshire).