A United U23s side, featuring a recovering Caolan Lavery, picked up a first Premier League Cup victory over West Bromwich Albion on Thursday night.
An injury time strike from Nathan Thomas saw the Blades to all three points in a tense encounter at Aggborough, home of Kidderminster Harriers.
The Blades started brightly with Smith having an effort well saved by the Baggies' goalkeeper on 10 minutes. For the remainder of the first half chances were at a premium with a Warhurst save from Clayton-Phillips shot from outside the area being the most noteworthy action.
After the break it would be Smith yet again knocking on Albion's door but was denied by House in the hosts' goal.
Chances were coming thick and fast for the Blades with Thomas striking the frame of the goal and Bennett having an effort fly just wide of the post as the deadlock remained.
United struck the woodwork again in the final quarter of an hour in search for a winner with Slater's shot cannoning off the crossbar.
However, four minutes into stoppage time, the Blades found the goal they'd been searching for with THOMAS picking up the ball on the right hand side, cutting in and curling home brilliantly and sealing the deserved win for United.
Blades: Warhurst, Bennett, Norrington-Davies, Graham, Heneghan, Ferguson, Gilmour, Slater, Lavery (Greaves 70), Thomas, Smith.
Unused: Dewhusrt, Cantrill, Broadbent, Doherty.