Two late goals saw the Blades slip to their first defeat in four games on Tuesday afternoon at the Steelphalt Academy.
The first chance of the game went the Blades way as Parkhouse picked up the ball inside the area and forced a good save from the Blues goalkeeper.
United kept up their early pressure as a cross to the back post found Clare but the forward couldn't steer his header on target.
The visitors would threaten just before the break with an effort from just outside the box forcing Dewhurst into a good stop low to his left.
After the break Potts almost found the opener as he got the ball out of his feet and struck a shot inches over.
Potts would again be involved just after the hour as he had another effort which was this time saved.
The opening goal would arrive with a quarter of an hour to go, a ball in from the right was met at the front post to put the Blues in-front.
Birmingham wrapped up the points with five minutes left to play as a shot low to Dewhurst's left found the bottom corner.
Blades: Dewhurst, Portman Withingham (Neal 25), Williams, Gordon, Belehouan, Potts, Broadbent, Parkhouse (Ompreon 45), Oure (Doherty 60) Clare.
Unused: Ogdan, Graham.