Ed O'Neil headed in Simon Russell's free kick on 17 minutes, before Russell himself added another in the 34th.
Billy Sharp pulled one back for the Blades 3 minutes before half time with a shot being deflected past young City keeper Curtis Aspden.
But midfielder Russell restored the two-goal lead just after half time. That's his fourth goal for the reserves since being told a fortnight ago he wouldn't be offered a contract after the end of the season.
Sharp pulled it back to 3-2 with his second of the game minutes later. Nathan Hotte had chances to seal it for City, but it wasn't to matter as it stayed at 3-2.
City line-up: Aspden, Matthews, Cattermole, Fry, Byron, Peat, O'Neil, Tomlinson, Donaldson, Hotte, Russell.
Subs: Cooper, Beattie, McGarry.
