United suffered a home defeat in Friday's televised top of table encounter, despite a positive first-half showing against West Brom.
David McGoldrick gave the Blades a deserved early lead, but Gareth Barry restored parity before the interval and Kieran Gibbs second-half strike swung the game in the Baggies favour.
For the home clash against Albion, boss Wilder named the team that finished last week's victory at Reading. Duffy and Sharp started, with Washington dropping to the bench, where he was joined by 20-year-old Sheffield prospect Smith, who was recalled from his loan spell at Barrow earlier in the week.
The Blades started positively, with Duffy forcing Johnstone to tip a dipping effort round the post. From the resulting corner, Egan rose highest, but under pressure his effort went well wide. In the 13th minute, United took a deserved lead though. Basham robbed Barnes to set the counter attack in motion and once in on goal MCGOLDRICK held off the attentions of Dawson before sliding past Johnstone.
United continue to force the issue, pushing West Brom back, but McGoldrick fired high and wide from another promising position. Albion's first meaningful effort on goal saw Barnes fire a free-kick wide, having being fouled by Norwood. The visitors then threatened from their first corner of the night, Phillips picked out Gayle, his effort was blocked before he fouled O'Connell.
With half-time approaching, the Blades broke at pace again and O'Connell's deflected effort almost nestled in the far corner, with Duffy again involved. But it was the visitors who hit back in the 41st minute, Barnes got the better of Basham and his pull back evaded everyone, but fell kindly for BARRY, who fired home left-footed. Henderson was then called into action to deny Phillips before proceedings were brought to a close.
The start of the second-half started in frantic fashion, Albion wanted a foul when O'Connell tangled with Gayle, but referee Simpson waved away their appeals and United almost caught them out at the other end, as McGoldrick got the wrong side of Dawson.
On 62 minutes, the visitors should have gone in front, Egan misread a bouncing ball, handled and was subsequently booked, book the advantage was played at Henderson saved United, denying Barnes, who had been played in by Gayle. Rodriguez then wasted an opportunity after good work by Barnes.
With 14 minutes remaining, West Brom got their noses in front through GIBBS, who slotted home after Barnes had teed him up from a Phillips. United could have levelled within minutes though, Baldock's cross fell nicely for Sharp, but from 14 yards, the skipper fired over.
Three minutes of added time were signalled, but United were unable to breach the visitors defence for a second time to rescue a point.
Blades: Henderson, Baldock, Stevens (Johnson 90), Fleck (Coutts 58), O'Connell, Basham, Sharp, Egan, Norwood, McGoldrick, Duffy (Washington 76).
Unused: Stearman, Moore, Smith, Cranie.
West Brom: Johnstone, Gibbs, Livermore, Phillips, Barnes (Brunt 90), Gayle, Barry, Rodriguez, Adarabioyo, Dawson, Hegazi.
Unused: Sako, Mears, Myhill, Townsend, Burke, Harper.