The hosts finally collected a victory - in their 18th game of the campaign - after a mental lapse from Newcastle captain Federico Fernandez, who swotted the ball away with his hand as he battled for the ball with Sharp in the area.
There was huge relief when the final whistle sounded seconds later and while Wilder still faces a monumental task to try to keep the club up, the mood of gloom hanging over Bramall Lane has been lifted, at least temporarily.
Sheffield United moved onto five points, leaving Chris Wilder's team nine from safety approaching the halfway point of the season.
'I understand that, especially watching the first half, we weren't good enough, and at the end of the day, I take responsibility for that, because I pick the team'. It was important we got a win soon.
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"We got the luck we deserved and saw it through".
"Everyone has written us off, the pressure is off".
The atmosphere around Newcastle has been hard since they were beaten by Championship side Brentford in the EFL Cup quarter-final and it became grimmer on Tuesday after the Sheffield United result.
"If Steve Bruce is saying that he has tried everything, then maybe what he is trying is not good enough and they do need to change".
The hosts' manager Wilder summed up his feelings after the whistle.
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"I felt we had an identity and it was us with the handbrake off, going for it and playing well in and out of possession", he said.
"I imagine the sending off and the penalty will be talked about, but in my opinion we were value for the victory tonight".
Darlow also did well to save from Bogle before Fraser picked up two bookings in quick succession just before the interval, the second for clipping McGoldrick. A long ball forward was contested between Sharp and Federico Fernandez in the box, with the Blades striker going down under the challenge.
"He did touch it with his hand - I gave him a nudge".
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