With Derby boss John Gregory suspended by the club pending what they described as "serious allegations", the Rams are in total disarray - and even though Neil Warnock's FA Cup semi-finalists were a little out of sorts, they still boasted too much firepower for their beleaguered opponents.
Blades goalkeeper Paddy Kenny was tested just once - and that the routine collection of a long-range drive - such was the lack of ideas and inspiration from the free-falling Rams.
United, though, were indebted to a moment of magic from Michael Tonge for the half-time lead - the 19-year-old scoring his eighth goal of the season in the 18th minute.
Owen Morrison's surging run was the catalyst, setting up Michael Tonge who initially jinxed his way past two Derby defenders before unleashing an unstoppable 20-yard, left-foot drive beyond a helpless Lee Grant into the goalkeeper's top left-hand corner.
Derby could have been further adrift as the interval approached but for Dean Windass' goal-bound header bouncing off Steve Elliott in the second minute - while Grant made saves from captain Rob Page, Steve Kabba and a lively Morrison.
But if Nick Chadwick had not miss-kicked Derby's best opportunity of an equaliser in the 41st minute with only Kenny to beat from 14 yards then the second half might just have been a different affair.
As it was when Steve Kabba slotted a defence-splitting Windass ball past Grant in the 55th minute for his eighth goal for the Blades this season the game was over as a contest.
The final scoreline should have been more emphatic. Windass struck a post after Grant had miss-hit a goal kick and the United striker also fired a Paul Peschisolido cross at the 20-year-old.