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.
Here are the best of today’s Championship rumours...
1. Lincoln City could revisit pursuit of Swansea City star
Lincoln City could reportedly look to secure a deal for Swansea City's Morgan Whittaker in January after a deal collapsed in the summer window. Jez George, the club's director of football, revealed the Imps would "love" to sort January deals for one or two of the players they missed out on in the summer. (The 72)
Photo: Alex Burstow
2. Middlesbrough consider swoop for Brazilian defender
Middlesbrough are reportedly interested in signing Brazilian right-back Heitor Rodrigues. Neil Warnock's side are set to bid just over £5 million but his current club Internacional are not willing to accept less than £10 million for the 20-year-old. (Football League World)
Photo: Silvio Avila
3. Borussia Dortmund considering move for another Birmingham City star
Borussia Dortmund are keen on Jude Bellingham's brother Jobe, who also plays for Birmingham City. The 16-year-old has featured for the Blues' U23 side this season. (Football League World)
Photo: Martin Rose
4. American businessman confirms interest in buying Derby County
American businessman Chris Kirchner has confirmed his interest in Derby County and has formally applied to the club's administrators. Kirchner is co-founder, chief executive and chairman of software company Slync.io, a global logistics technology provider. (Derby Telegraph)
Photo: Ashley Allen