United's Under 23s fought to come from behind with a superb second half performance which saw goals from Reece York and Jake Young overturn a 1-0 half-time deficit.
Kyle Hurst had given Birmingham City the lead with a brilliant strike after half an hour but United came out for the second half like a different team and turned the game around.
It was actually the Blades who had the first chance when Harry Sheppeard, who caused Birmingham no end of problems, stabbed an effort just wide after some good build up play.
But the hosts went on to have the better of the first 45 minutes, Jordan Amissah had to be alert to tip over a deflected effort off Joe Redmond before getting down well to stop McGilp's low effort.
It was Hurst who gave the hosts the lead though, the tricky turning sharply and bending a great effort into the far corner, leaving Amissah with little chance.
Despite the hosts being on top, it was United who had the two best chances of the half. Firstly, George Broadbent fired over from the edge of the box when he was picked out by Sheppeard before Jordan Hallam fired wide completely free at the back post from Stephan Mallon's cross.
United needed a big second half and they provided it, showing more positivity and intensity from the first whistle.
Hallam saw an effort deflected wide after move good work from Sheppeard, before Sheppeard finally got the assist he deserved just minutes later when his pull back was smashed home by York.
Sheppeard himself fired over immediately after as United went on the attack to look for a winner. Sheppeard then saw an effort blocked before Michael Luyambula saved York's follow up before Jake Wright was withdrawn after an hour on his return.
It felt like a winner was coming and it arrived with 20 minutes to go. Sheppeard once again got free down the right, this time his cross was parried for Young to bundle home from close range with his first touch of the ball.
Amissah was rarely troubled in the second half and the closest Birmingham came to a leveller was when substitute Tom Anderson fired high and wide from a cross with ten minutes to play.
Blades: Amissah, Williams, Doherty, Neal (Young 65), Wright (Cantrill 60), York (Brunt 86), Sheppeard, Broadbent, Oure, Hallam, Mallon.
Unused: S. Kelly, Gaxha.