The win pushes Sean Dyche's side five points clear away from the relegation zone.
Sheffield on the other hand still sit bottom of the Premier League with just two points from 16 games.
Nick Pope: 8/10- In typical Burnley fashion, the side picked up an early goal then sat back, this tactic can only work with a top keeper in goal.
Although Pope didn't have to pull of any world class saves, his importance to the result can't be underestimated as he saved everything put before him with relative ease.
Matt Lowton: 6/10- Lowton was booked early on but dealt with it well, sitting off his various individual opponents.
His long balls forward to Wood and Barnes were important to help the Clarets get out when under heavy pressure.
Ben Mee: 8/10- The captain led by example grabbing the opener as he headed home Robbie Brady's deep corner.
James Tarkowski: 7/10- It was a usual performance from Tarkowski, strong at the back, dominant in the air and calm on the ball.
Charlie Taylor: N/A- Taylor managed just nine minutes before being subbed off due to injury, making it impossible to rate his performance.
Youngster Josh Benson came on in the right midfield spot, meaning Erik Pieters moved to left back and Brady moved to the left side of midfield.
Erik Pieters: 6/10- Pieters was solid once moved to left back, a position he hasn't played for a while. He was solid and looked hard to beat as he completed a compact Burnley backline.
Ashley Westwood: 6/10- Westwood did what he normally does, provide Dyche with a crucial yet understated performance.
His ability to pick up lose ball, defend from midfield and transition the ball form deep midfield helped Burnley push through United's pressure
Josh Brownhill: 7/10- Not only was Brownhill the ever present workhouse for Dyche's midfield, he also denied Sheffield United from scoring the first of the game, blocking Rhian Brewster's effort from a corner.
Robbie Brady: 7/10- It was Brady's corner that Mee converted and his deep delivery caught out the United defense. He was move to his preferred side early on in the game and did a good job.
Two up top
Ashley Barnes: 6/10- Barnes was subbed off with just over 10 minutes to go as Dyche bought on Dale Stephens in order to go more defenive.
Branes was his usual self and proved a handful for the Sheffield backline. However, Branes failed to create any clear cut chances.
Chris Wood: 6/10- Like his strike partner Barnes, Wood was relatively quiet tonight. He provided Burnley with an outlet and gave the defense something to aim for when clearing the ball.
Josh Benson: 6/10- Benson settled in well after his early introduction to the game and didn't look out of place in a match full of experienced players.
Dale Stephens: 6/10- Stephens didn't have long on the pitch and came on for Barnes to keep the Clarets defensive solidity, which he did well.
Aaron Ramsdale: 6/10- Ramsdale had little to do apart from save Mee's header, which he couldn't.
Chris Basham: 6/10- Basham was active at the back and passed out well from the back to initiate Sheffield's attack.
John Egan: 6/10- One of Sheffield United's better players, Egan provided an attacking threat from deep, and even had a few chances on goal.
Jack Robinson: 5/10- Robinson was subbed after 55 minutes, making way for John Fleck as Chris Wilder looked to change his formation.
George Baldock 5/10: Probably the weakest one of Sheffield's back three, Baldock did his job but looked the one Burnley could exploit going forward.
Ethan Ampadu: 5/10- Ampadu was another one who was subbed off as Wilder chased the game. His defensive nature and natural style didn't suit United going forward.
Ampadu did nothing wrong in his time on the field but was replaced by Oliver Norwood with 25 minutes left.
Ben Osborn: 5/10- Osborn was quiet and offered little and struggled to keep up with the battle being provided from Westwood and Brownhill.
Enda Stevens: 6/10- Stevens offered the Blades versatility both going forward and at the back. He had a few minor chances on goal and covered his area of the pitch well.
David McGoldrick: 4/10- McGoldrick was player just behind the two strikers, but this didn't work against Burnley.
The Clarets sat deep meaning McGoldrick struggled to break through or split the defense whist playing in the 'number 10' role.
Rhian Brewster: 6/10- Brewster was United's main attacking threat, providing the Blades with their best opportunities, including the one cleared off the line by Brownhill.
Lys Mousset: 5/10- Mousset was subbed off just after the hour mark for Oliver Burke.
Mousset offered little going forward and although having both Mee and Tarkwoski's number when it comes to pace, he failed to use it to his advantage.
John Fleck: 7/10- Fleck was the first of three Wilder substitutes and changed the flow of the game when he came on.
Once introduced t the game, Fleck helped with the transition of the ball going forward for United, through Burnley's solid banks of four.
Oliver Burke: 7/10- Burke came on and immediately gave the hosts something to think about.
His pace allowed him to make runs through the Burnley backline that others couldn't make, although nothing came from them.
Oliver Norwood: 5/10- Norwood came on to add even more attacking pressure to Burnley but failed to create anything clear cut.
Although he had a fair bit of the ball he couldn't make a difference to the game.