Albion welcomed the in-form Blades looking to end a terrible week on a high – after back to back defeats on the road at QPR and Southampton.
The first half was less than inspiring – as in front of a low crowd at The Hawthorns both sides struggled to create clear cut chances.
In the second Albion fired out of the blocks though – as Aune Heggebo’s seventh goal in seven games was followed by a superb strike from Karlan Grant.
Albion dominated the visitors and could have added to their tally.
It was a half of football that left Wilder, who was once close to landing the job at Albion, furious.
He laid into his players and said they failed to show the fight that Albion did – and hailed the Baggies’ players for ‘fighting for their manager’, after a difficult run of results.
He said: “That is as angry as I have been in a long time, I’m frustrated and annoyed with our second half.
“They just thought the game would come to them, they’ve got to go and fight.
“We’ve been on runs and environments and atmospheres in games, and there was an opportunity with the run West Brom have been on.
“We smelt it before the game, it was quiet, there was a vulnerability regarding the opposition in my opinion, we smelt it.
“It is alright smelling it, you have to get after it and bury them and we didn’t do that.
“They are a group who are fighting for their manager to get a result.
“It could have been three or four, there was a massive drop off.”