United exited the FA Youth Cup in the fourth round with a second half strike from Jordan Clarke being enough to send Birmingham through to the next round.
The Blades worked tirelessly at a snowy St. Andrew's but couldn't progress to the next stage of the competition.
The first half hour was very cagey as both teams attempted to find their feet with long shots that failed to trouble either goalkeeper being the most noteworthy action.
A chance would arrive, though, on 37 minutes as Clarke turned his man inside the United area and got a low shot away but Dewhurst was on hand to turn it around a post to keep the tie goalless.
After the interval the Blades had their first real chance of the night as a free-kick cleared by the Blues defence fell to Oure on the edge of the area, who struck, on the half-volley, into the side netting.
Dewhurst would be forced into another good save before the hour mark as another long range effort from City, this time from Stirk, had to be pushed over.
The deadlock would be broken on 65 minutes by Birmingham as Stirk played a through ball into CLARKE who got inside the box and placed the ball into the bottom corner to give the Blues the lead.
As time was running out the Blades pushed forward in search of an equaliser and after winning the ball in midfield it was sent to substitute Capello in the area, who went over from a challenge from Dawes but appeals for a penalty were waved away by the referee.
With just a minute to go United had a golden chance as a great cross from the right found Graham who had to stoop low to make the header but the ball went over the crossbar from close range in what was the final opportunity of the tie.
Blades: Dewhurst, Portman, Boyes, Gordon, Cantrill (Williams 23, Capello 75), Graham, Broadbent, Slater, Parkhouse, Doherty, Oure (Potts 67). Unused: Warhurst, Ompreon.