Thomas Gaardsoe scored the winner with five minutes to go, after Darren Moore had scored at both ends.
The first chance came when Jason Koumas swung in a wicked corner from the right, which Blades keeper Paddy Kenny tipped away from under his crossbar.
In the 22nd minute, Koumas broke clear from just inside the Albion half after a corner had been cleared.
His mazy run left the defence trailing in his wake and the winger kept his balance under Nick Montgomery's challenge before then putting his shot wide of Kenny's left post after having done all the hard work.
United striker Paul Peschisolido squandered a chance on the half-hour when he got behind the Albion defence and twisted into the box, before shooting into the side-netting.
Rob Kozluk almost opened the scoring for the hosts in the 36th minute with a right-foot volley from 30 yards which sailed wide of Joe Murphy's left post.
Lee Hughes should have put Albion ahead two minutes later when he was one-on-one with the goalkeeper after a mistake by Kozluk, but fired his shot at Kenny, who gathered comfortably.
The Albion striker then missed by inches at the end of the half when his left-foot shot beat Kenny this time, but went wide of the post.
It was Sheffield United who took the lead 12 minutes into the second half.
Montgomery crossed from the right after Murphy had failed to gather the ball under pressure from Ashley Ward.
It bobbled across the front of goal and the luckless Moore chested it over his own line under the close attention of Peschisolido.
Moore soon made amends for his own goal when he levelled for the Baggies on 70 minutes. His powerful header from a Koumas corner took a slight deflection, before beating Kenny to his left.
The Baggies went ahead in the 85th minute when Gaardsoe converted from Joost Volmer's low cross after Koumas had turned the ball back into the box following Kenny's spectacular save from Sean Gregan's shot.
Kenny then pulled off a brilliant stop from Koumas in the final minute after the winger had turned Mike Whitlow inside out.