Derby County's reward for beating the freezing temperatures was a vital victory, which put United's promotion push on ice.
Second-half goals from young strikers Marcus Tudgay and Izale McLeod secured three precious points to lift George Burley's team out of the relegation zone.
Derby also had the bonus of seeing arch-rivals Nottingham Forest replace them in the bottom three of Division One.
Afterwards, Burley said: "We knew it was going to be a very tough game against a very good side, but overall we deserved the three points and now we must keep building on this." United manager Neil Warnock said: "Our performance was like the weather, a bit damp and miserable. We just weren't up for it." Derby certainly were and the new players Burley has drafted in over the last few weeks have made an impact.
On-loan Everton midfielder Leon Osman had a promising debut while Marco Reich again looked a top class player.
It was the German's superb cross that set up Derby's opener and he was also at the heart of most of his team's best moves.
But Derby's defence was also impressive with Youl Mawene giving one of his best performances.
United faded after a promising start and their best chance brought a fine save from Lee Grant who did well to keep out a Mark Rankine header in the 26th minute.
Osman wasted Derby's best opening in the first half but Tudgay made no mistake in the 70th minute when Reich flighted the ball in from the left and his header had too much power for Paddy Kenny to keep out.
Substitute Jonathan Forte shot wide in the 88th minute for the Blades but Derby sealed victory in stoppage time.
Paddy Kenny made a hash of trying to clear a Chris Morgan back pass and McLeod took the ball away from the keeper before steering a right-foot shot in from a tight angle.