It was an action packed first-half which saw the hosts go into a two-goal lead inside the opening 15 minutes.
After Blues failed to deal with a corner, the ball fell to Shaun Miller and his tame effort managed to find a way past Nick Townsend.
The Blades doubled their advantage after 12 minutes, once again through Miller. The striker beat the offside trap and rounded the Blues 'keeper before slotting the ball into an empty net.
The visitors had Townsend to thank moments later after he acrobatically tipped over Harry Bunn’s headed effort.
Blues clawed one goal back through Reece Hales after some fine work from Patrick Antelmi. The striker robbed Sean McGinty on the edge of his own box, played the ball to Hales who sent a composed finish past Mark Howard.
The comeback was complete five minutes before the break. Liam Truslove found himself in space 20 yards from goal and when the ball came to him he struck a powerful effort into the bottom corner.
Koby Arthur went close to giving his side the lead in the early stages of the second-half. The midfielder slalomed his way into the penalty area and crashed a shot against the foot of the post.
United then began to assert themselves on the game and created of number of chances on goal. Harry Bunn struck the crossbar before Jahmal Smith forced Townsend into a brilliant save.
The best chance of the afternoon fell to Shaun Miller who, on a hat-trick, blazed over from six yards.
Blues made their opponents pay with 20 minutes remaining. Koby Arthur picked up the ball, cut inside and unleashed an unstoppable effort into the top corner.
The hosts tried to force an equaliser but the Blues defence stood firm to see out an impressive comeback.
Blues XI: Townsend; Kalenda (Dacres-Cogley 45), Kelly, Bell, Moseley; Arthur, Webb, Truslove, Soloman-Otabor (Cooper 90); Antelmi (McGee 60), Hales.
Unused subs: Preston, O’Neil.