United suffered a setback in the pursuit of automatic promotion, as Bristol City edged an entertaining contest at Bramall Lane.
United led twice through Billy Sharp and Scott Hogan, but Andreas Weimann's hat-trick swung the game decisively in the favour of Lee Johnson's side.
For the clash against the Robins, boss Wilder made just one change, with Dowell replacing Cranie, who dropped to the bench, with Johnson and Washington also named amongst the substitutes.
United were characteristically quickly out of the blocks. Basham charged forward and fed Sharp who was denied at the expense of a corner, from which the skipper headed wide at the back post. But in the sixth minute SHARP wasn't to be denied. From Fleck's inch perfect delivery, United's number ten was jogging on the spot to head home, despite Diedhiou claiming a foul.
The Blades continued to pour forward, with McGoldrick drawing a save from O'Leary. Hunt became the first player to be booked, for a cynical foul on McGoldrick. The visitors were gradually getting into the game and Henderson was at his best to deny Brownhill from distance, tipping behind at full stretch.
Pack was then booked for another mistimed lunge; this Norwood was the victim. And on the half hour City levelled. Hunt found space for a cross on the right and WEIMANN managed to beat Henderson with a looping header, with the Blades goalkeeper seemingly losing the flight of the ball in the sun.
United looked to hit back, but O'Leary claimed Norwood's near post cross, with Sharp lurking. Four minutes of added time were signalled and in the first of those, O'Connell headed over at the back post from another inch perfect delivery from Fleck. The last saw Weimann have a debatably free-kick comfortably saved by Henderson.
At the break, United made a change with Hogan replacing Dowell, a switch that saw McGoldrick drop into a deeper role. But it was City who started the second-half the better, with Smith having a shot saved by Henderson, the Blades stopper then had to be alert to deny Weimann.
The home faithful were attempting to rally the players and it almost paid dividends as Fleck fired an effort at goal that was saved by O'Leary. At the other end, the woodwork saved the Blades after Norwood was booked for a foul on Weimann, with Brownhill's shot hitting the post with Henderson rooted.
And Bramall Lane exploded into a sea of celebration in the 71st minute, as HOGAN nodded home his first for the Blades after Baldock had done excellently to stand Dasilva before delivering to the back post, with Sharp also involved in the build-up.
With 14 minutes left, an injury forced a United reshuffle, with Johnson replacing O'Connell and moments later City restored parity for a second time, with WEIMANN adding the finishing touch at the back post from Palmer's cross.
Then on 83 minutes WEIMANN completed his hat-trick, linking up with Diedhiou and getting the better of Stevens, before firing past an onrushing Henderson. Six minutes of added time were signalled, moments after O'Leary and Webster wasted time after a foul in their box.
United ploughed forward and Hogan thought he'd found space for a second, only for City to force it behind for a corner, from which McGoldrick headed over, with Henderson up to add support to the attack, but ultimately it was in vain as the visitors held on.
Blades: Henderson, Baldock, Stevens, Fleck, O'Connell (Johnson 76), Basham, Dowell (Hogan 45), Sharp, Egan, Norwood, McGoldrick.
Unused: Coutts, Stearman, Moore, Cranie, Washington.
Bristol City: O'Leary, Dasilva, Webster, Wright (Palmer 73), Smith (Paterson 73), Brownhill, Diedhiou, Weimann (Baker 86), Pack, Kales, Hunt.
Unused: Taylor, Kelly, Eliasson, Marinovic.