United's Under 23s had to dig deep to beat top of the league Birmingham City thanks to a Nickseon Gomis goal 13 minutes from time at Bramall Lane.
Looking to bounce back from last week's disappointing defeat at Crewe, United found themselves on the back-foot for plenty of the encounter but defended brilliantly and took their chance when it arrived.
There were very few chances to speak of during a frustrating first half which saw the visitors have plenty of the ball but rarely test Jake Eastwood in the United goal.
Eastwood did have to be alert to push over a free-kick from Beryly Lubala after 15 minutes but that was really the only chance either side fashioned in the opening 40 minutes or so.
But United did have the best chance to go ahead shortly before the break when Harry Sheppeard found a yard down the right and put in a perfect ball for Jordan Hallam, the striker not making clean contact and scuffing the ball towards goal and allowing Connal Trueman to push behind for a corner.
The second half started much the same with very few chances to speak of for either side approaching the final 25 minutes of the game.
Eastwood did well again to react to a header from a corner down low before holding another free-kick from Lubala, this one on the edge of the box, before the introduction of Jake Young gained the Blades some much needed momentum.
With 15 minutes to go, Young rolled his man out on the wing, charged towards the goal but scuffed his effort well wide and beyond an open Simeon Oure who could have had a tap-in.
But it mattered little just three minutes later when United found the crucial breakthrough. Hallam's free-kick floated into the box was flicked on and in came Gomis at the back post to hammer home into the back of the net.
Birmingham spent the final 10 minutes putting plenty of pressure on United but a brilliant defensive effort saw the Blades hold on for a hard-fought and important three points.
Blades: Eastwood, Ferguson (Young 62), Cantrill, Mingi, Graham, York, Sheppeard, Greaves, Oure (Potts 82), Hallam, Gomis.
Unused: Dewhurst, Ackroyd.