Goalkeeper Nick Pope made a welcome return to a after almost five months out as he helped the Clarets go top of the table.
The England international completed his first 90 minutes since suffering a dislocated shoulder in the Clarets' Eurpoa League tie at Aberdeen at the end of July.
And he played his part as Steve Stone's men bounced back from a first defeat in nine games to Leeds a week ago to go above the Yorkshiremen, who lost at home to Barnsley earlier in the day.
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United’s line-up boasted over 350 professional appearances through Kieron Freeman, John Lundstram, Kean Bryan and former Clarets defender Daniel Lafferty.
But it was Burnley who took the lead with 18 minutes played through Dwight McNeil’s excellent strike.
The home side equalised when Stephen Mallon fired in from close range but the Clarets snatched the lead again just before the break through Dan Agyei.
And Agyei notched his second of the afternoon just after the hour mark to put the game out of sight of the Blades.
The win ensured Burnley finish the year level on points at the top of the Professional Development League's northern division - although Birmingham City's win later in the day edged the Clarets down to second spot on goal difference.
The first chance of the game fell to the Blades, as Reece York’s back-post header from Mallon’s cross was kept out by Pope.
And Stone’s men that struck first as McNeil drove forward from midfield before rifling an effort into the top corner to give the Clarets the lead.
The visitors came close to adding a second moments later as Pope sparked a counter-attack with a long throw finding Agyei, who then picked out Josh Benson on the left. The central midfielder returned the ball into the area for Agyei who hit the post from close in.
However, United then grabbed an equaliser with 35 minutes gone as Lafferty cut the ball back to Mallon to fire past Pope.
The Clarets weren't level for long, though, and regained the lead a minute before the break as Agyei stabbed the ball over the line from close range, following a corner.
It was a much quieter opening to the second half, with neither side having any real chances until Agyei was put through on goal 20 minutes in before slotting past Jake Eastwood to double Burnley's advantage.
And the pacy forward came close to securing his hat-trick with an effort disallowed for offside.
Despite the Blades' best efforts at getting back into the game, the Clarets did well to keep the Yorkshire side at bay, Pope standing form to safeguard the points and take Burnley to the top.
Burnley: Pope, Cropper Younger, Glennon, Koiki, Bayode (Blair 40), Benson, McNeil, Harker, Agyei, Chakwana. Substitutes: McMahon, Cook, Howarth, Trialist.
Sheffield United: Eastwood, Belehouan, Bryan, Doherty, Graham, York, Freeman, Lundstram, Smith, Mallon, Lafferty.