Matthew Kilgallon netted his first goal for the Blades last Saturday; his goal was enough to beat Barnsley 1-0 in the South Yorkshire Derby at Bramall Lane.
The former Leeds United defender headed home Keith Gillespie's free0kick past Heinz Muller. Blades goalkeeper Paddy Kenny pulled off a great save to deny Hungarian striker Istvan Ferenczi in the second half.
For spells the visitors put the Blades to the sword but United defended well in Gary Cahill's final game to win their first Derby of the season.
Blades boss Bryan Robson said; "We need to get good results if we want to be in that top six towards the turn of the year.
"Today is a good start because Barnsley battled hard. It's a good three points.
"It was a typical local derby, it was end-to-end stuff and was a battling performance from both sides."
Meanwhile opposition boss Simon Davey believed that his Barnsley side did enough to leave Bramall Lane with a point; "It's the same sort of report from the Sheffield Wednesday game away - I thought we deserved more.
"I didn't think it was a free-kick that they scored off and we had a great chance a little bit before that when Paddy Kenny pulled off a fantastic save.
"So on reflection I'm very disappointed yes."