Jordan Hallam scored four times as United returned to winning ways in the Professional Development League on Monday.
Tyler Smith was also on the scoresheet as the Blades gained a first victory in seven matches in all competitions to boost hopes of a top-two finish.
HALLAM had already stung the palms of City stopper Wollacott, before opening the scoring in the 18th minute, scoring on the angle after good build-up play involving Brooks and Smith.
And just after the half hour, the lead was doubled. Some goog work down the left, saw Brooks and Kelly combine to cross for SMITH to bundle home from close-range at the second attempt.
The Blades continued to be the dominant force for the remainder of the first period, but didn't extend the lead further until the 62nd minute.
HALLAM got his second of the game from the penalty spot after being hauled down by Lyons-Foster. And 12 minutes later, HALLAM completed his hat-trick, slotting the ball under Wollacott after a fine run and pull back from Brooks.
The Robins were reduced to ten men as the clock ticked past 90 and deep into stoppage-time their misery was compounded as United hit a fifth. Hirst showed persistent and determination to keep the ball in play and having beat one defender he was bundled over for another penalty. HALLAM stepped up and lashed home despite the best efforts Wollacott.
Blades: Eastwood, Bennett, Kelly, Reed, Graham (Ferguson 68), Cantrill, T. Smith (Charlesworth 76), Slater (Gilmour 59), Hirst, Brooks, Hallam.
Unused: Warhurst, Doherty.