United's Under 23s overcame Bristol City in a thrilling five-goal affair on Saturday morning and had to come from behind twice to seal the points.
Two goals from half-time substitute Sam Ackroyd and a goal from Harrison Foulstone were enough on a day where the Blades undoubtedly made life difficult for themselves.
They should have been 1-0 up inside the first five minutes when Jake Young lobbed Lochlan Robertson but his effort just dropped over the bar.
United were well on top in the opening 15 minutes but were hit on the break as Louis Britton headed home the first of two goals during the game.
There was a lot of good play from the Blades but the chances weren't following but it always felt like the goals would arrive as the game entered the second half.
United didn't have to wait long for an equaliser when half-time substitute Ackroyd had an instant impact, taking down Zak Brunt's cross and firing low into the far corner.
Tails were up and it should have been two when Young scuffed wide from close range, Bristol going up the other end and retaking the lead through another Britton header no more than 60 seconds later.
But the Blades wouldn't give up and fought their way back into the game in the final 25 minutes. A good move saw Jake Kelly slide in Foulstone down the left and the full-back did the rest with an excellent low finish into the corner.
Ackroyd had the ball in the net and appeared to have been denied a stonewall penalty, but a spot kick did come when substitute Sammy Ompreon was fouled inside the box, allowing Ackroyd to step up for his second of the game.
Bristol had one big chance with the final kick of the game but United could and should have scored more on the day, but it was a big three points on the road.
Blades: S. Kelly, Williams, Foulstone, Neal, Gomis, Broadbent, J. Kelly, Richardson (Ackroyd 46), Young (Gaxha 81), Brunt, Fleary (Ompreon 63).
Unused: Chapman, Skerritt.