James Beattie's first half header flew past West Brom keeper Dean Kiley on 35 minutes.Nathan Ellington went close for the Baggies just before the break.
Blades keeper Paddy Kenny had to make several superb saves to keep United in the game.
Here were the teams...
Sheff Utd:Kenny, bromby, Morgan, Kilgallon, Geary, Gillespie, Tonge, Montgomery, Armstrong, Beattie, Sharp.
West Brom:Kiely, Hofkens, Barnett, Albrechtsen, Robinson, Morrinson, Greening, Pele, Teixeira, Beattie, Phillips.