The Blades found themselves 1-0 down on 17 minutes when James Milner headed down to Obafani Martins who shot past Paddy Kenny from the edge of the area.
United slowly battled and it was some time before the equaliser came, substitute Christian Nade took advantage of a goalmouth scramble to net his fourth goal of the season on 74 minutes.
Six minutes later disaster struck when Steven Taylor rose highest to head home a Keiron Dyer corner.
"I am distraught but I have to keep my chin up." Said Blades boss Neil Warnock.
"We had some great chances but we gave away two elementary goals and we got punished because of that.
"They've not had to work hard for the win. When we equalised I didn't expect them to score a goal from a corner. But the Premiership is so unpredictable."
Opposition boss Glenn Reoder was naturally happy about the victory as the three points more or less secure there Premier League status for at least one more season.
Reoder said; "If people are honest with themselves they did not expect that to happen today.
"I believe it was only inside our dressing room that we believed we could come here and win.
"People have looked at us and thought, at times away from home, we're not hard enough. That gave them the motivation to come out fighting."