The Blades went 3-0 up thanks to a brace from Lys Mousset and a third from Ben Osborn, however their Yorkshire rivals fought back with two goals of their own inside four minutes.
Barnsley hoped they could perform an exceptional comeback, however Sheffield United held on right till the end and claimed all three points.
The win took Slaviša Jokanović’s side up to 14th in the Championship on 18 points – only three away from the top six.
They now face a tough test in newly-promoted Blackpool, who have enjoyed a successful start to the campaign and sit three points ahead.
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The win took Slaviša Jokanović’s side up to 14th in the Championship on 18 points – only three away from the top six.