The Tykes were without Danny Drinkwater following his departure for Leicester City and midfielder Jacob Butterfield (knee) is ruled out for the season. Craig Davies returned to the side but winger Jim O’Brien missed out after a groin injury. Nathan Doyle was not included.
Darius Henderson fired the visitors in front from the penalty spot on 36 minutes, before adding a second three minutes later.
The former Blades striker completed his hat-trick on his return to South Yorkshire with 15 minutes to go.
Jimmy McNulty replied late on for Barnsley.
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