Albion are back in home action again on Wednesday night when they entertain Frank Lampard's Coventry City, before a Sunday lunchtime date at Watford.
The Blades have another tough road trip on Wednesday, at Millwall, followed by Saturday's home game with Wayne Rooney's Plymouth Argyle.
West Bromwich Albion head coach Carlos Corberan told BBC Sport:
"We lost concentration in the box to allow them to score their two goals. It is frustrating.
"In the second half we managed to get back to how we performed in the first 20 minutes."
Sheffield United boss Chris Wilder told BBC Sport:
"We were up against a really good team. We knew this was a massive test for us. and we showed great character to overturn a lead the way we did.
"So I'm delighted with that. As far as I'm concerned, that's our best, hardest-earned point of the season. It was so important we got something.
"We could easily have decided it wasn't going to be our day, let's get back on the bus and get home and get in front of the fire. But they didn't.
"It was tough out there. But this side are learning on the job. We had six 22-year-olds on the park at one stage playing against men, in men's conditions. But they fought back and got a result."