Sheffield United: This is what being a Blade is all about
Deployed in midfield rather than his preferred position of centre-half, Basham overcame a difficult start to Saturday's Championship showdown at Elland Road before firing past Kika Casilla midway through the second-half.
Despite admitting he had contemplated withdrawing the 30-year-old during the interval, Wilder claimed Basham's persistence and doggedness provided the perfect example for his team mates to follow as they chase automatic promotion to the Premier League.
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Hide Ad"Bash, for me, showed out there what a Sheffield United player is all about," Wilder said. "He showed what it takes to be a Sheffield United player in this squad and the type of approach we've always wanted our squad to have.
"He didn't play well to begin with and, yes, we were thinking about a change at one point. But he kept on going, he kept on driving away and he dug himself out of a hole."
"That's what you've got to do," Wilder added. "If you're in a hole, you've got to give everything to dig yourself out of it and you've got to have people around you willing to help. That's what we saw out there."
United found themselves under pressure throughout much of the opening period as Marcelo Bielsa's side seized control of the contest. Martin Cranie, deputising for Basham at the back, justified his selection with an important block to deny Patrick Bamford before Jack Harrison fired over the crossbar.
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Hide AdHowever, as the contest wore on, the visitors began to establish a foothold in the game and their patience was rewarded when captain Billy Sharp sent Basham darting into space after escaping Liam Cooper's clutches.
The result lifted United to second in the Championship, four points behind leaders Norwich with eight fixtures remaining and one above Leeds, who slipped to third.
"Yes, they came right at us and had chances," Wilder conceded. "I'm not embarrassed to say that because they're a good side and they are right up there for a reason, like I made clear beforehand. But we showed a real desire too.
"Bash, and all the rest of the lads, were full of it."