United exited the County Cup at the third round, following a disappointing loss on Sunday.
The tie, which had been previously postponed before Christmas, only just passed a lunchtime pitch inspection at the War Memorial Ground.
Having beaten Bradford City in a friendly at Shirecliffe on Friday, the Blades chose from a full strength squad.
Oughtibridge are rising through the division and are currently third in the East Midlands Premier League, the division United topped last season.
United started slowly and were punished twice inside the opening 25 minutes.
The Blades struggled in the opening hour of the contest, but a goal from substitute Nat Shaw made it 2-1 shortly afterwards.
But a straight red card for midfielder Spurr meant the Blades were unable to complete the comeback.
Blades: Houldsworth, Robinson, Neary, Marshall, Barker, Bell, Spurr, Hartley, Brown, Marsden, Pearson.