James Beattie headed home after Chris Armstrong crossed to score the only goal of the game and claim a first league win for new manager Bryan Robson.
Billy Sharp, who was missing in the 1-0 defeat at Watford last weekend returned to the starting line-up to partner Beattie upfront.
But it was the Baggies whose attacking prowess created the game's first chance, which fell to Scotland international Craig Beattie in the 11th minute after Kevin Phillips picked out his run with a measured cross from the left only for the former Celtic striker to mis-time his volley which looped up on to the bar before being gathered by a grateful Paddy Kenny.
The home team soon found their feet and if it was not for Dean Kiely they would have been ahead after Chris Armstrong turned on the edge of the box and fired in a thunderous drive that had to be firmly turned away by Kiely.
It was not until the 35th minute that the deadlock was broken when Armstrong's cross found Beattie in space at the back post and the ex-England striker made no mistake in re-directing his header back across goal and beyond the sprawling Dean Kiely.
The Yorkshire team emerged from the tunnel after half time obviously intent on increasing their lead and it took two timely blocks from Leon Barnett and Martin Albrechtsen to deny them of another goal.
The West Brom defence became more fragile as the pressure mounted and a misunderstanding between Kiely and Albrechtsen almost allowed veteran winger Keith Gillespie to capitalise.
Tony Mowbray was clearly frustrated by his team's lack of ingenuity and introduced Nathan Ellington and Zoltan Gera for the hapless Craig Beattie and the ineffective Pedro Pele in an attempt to inject some urgency into his team's performance and his plan almost came to fruition but Andrade Filipe Teixeira's diving header hit the side netting.
Michael Tonge could have sealed the victory for the Blades in the 78th minute and should have done better when his half-volley from the centre of the area flashed wide of the West Brom goal.
Beattie was unlucky not to double the lead late on and keeper Kenny had to be alert on two occasions in the closing stages to deny West Brom an equaliser but Robson's men survived a frantic final period to ensure that they secured their first Championship win of the season.