The international break and a late goal halted United's four-game winning streak.
A flicked header by substitute Marley Watkins secured the points for Bristol City.
Boss Wilder was forced into a change with Fleck still struggling with a groin issue. Lundstram started. New boys Johnson and Washington were on the bench and joined by the fit-again Clarke and Baldock.
United failed to replicate the blistering starts prior to the international break, in fact Bristol City were the quickest out of the blocks, creating a chance on four minutes but Henderson parried away from Eliasson and Dasilva scuffed the rebound.
Lundstram was forced into a decisive defensive header as United took time to get the neat, crisp passing game back to the fore. The visiting side's first chance arrived on 15 minutes with McGoldrick lashing wide from the edge of the box after a link up with Sharp.
A fizzed Norwood free-kick was headed wide and another left-footed McGoldrick effort was wide after Sharp took the attentions of two defenders.
An even first half ended with off target headers at both ends. McGoldrick connected with a Norwood free-kick but the ball drifted wide and Diedhiou could not trouble Henderson from Dasilva's cross.
United created the first chance of the second half but Lundstram's curler was pushed away by goalkeeper Maenpaa. The Blades also had a penalty appeal turned down when Kalas caught Stevens but no spot-kick was forthcoming.
Diedhiou headed wide and then got around the back of the defence but lashed a half-volley wide, whilst Weimann's flicked header was also wide as the Blades faced a little pressure.
Johnson and Washington were introduced but City's chances continued. Weimann's effort was blocked in a crowded penalty area after a Pack free-kick.
The decisive moment came as the game entered the final ten minutes. Weimann's shot struck Stevens and City's penalty appeals were waved away. However, from the resulting corner, a flick on from WATKINS found the top corner, giving Henderson no chance.
Wilder threw on Clarke but the best opportunities fell to the other substitutes as City protected their goalkeeper well. Washington headed wide an Egan cross and deep into injury-time Johnson sliced over.
Bristol City: Maenpaa, Dasilva (Watkins 62), Webster, Brownhill, Diedhiou (Taylor 78), Weimann, Kelly, Eliasson (O'Dowda 62), Pack, Kalas, Hunt.
Subs: Baker, Walsh, Paterson, O'Leary.
Blades: Henderson, Stevens, O'Connell, Basham, Lundstram (Clarke 83), Sharp (Johnson 68), Egan, Norwood, McGoldrick, Freeman, Duffy (Washington 68).
Subs: Baldock, Woodburn, Stearman, Moore.