James Tarkowski led by example as captain in the Premier League for the first time, although his goal wasn’t quite enough to give the Clarets a hat-trick of wins.
Tarkowksi, taking the armband from the injured Ben Mee and a commanding figure at both ends of the pitch, fired Burnley into a half-time lead as they looked to go above Sheffield United and stay in an improbable race for Europe.
Sean Dyche’s side were just over 10 minutes from moving up to eighth place in the table until John Egan levelled for the Blades.
But even though a 14th clean sheet and record-equalling 14th Premier League win just eluded them, the Clarets have still lost just once in their last 11 league games and despite missing more key men delivered another defiant performance which keeps them on course for a fantastic finish.
The Clarets, already stretched by injuries, were hit by a further blow as Mee’s ever-present record was ended by a thigh problem and Jack Cork succumbed to the ankle injury he sustained in Monday night’s win at Crystal Palace.
That interrupted Mee’s defensive partnership with Tarkowski for the first time in 57 Premier League games as Kevin Long returned to Burnley’s starting line-up for the first time in the top flight since December, 2018.
There was good news, however, in the shape of a return on the bench for top scorer Chris Wood and widemen Johann Berg Gudmundsson and Robbie Brady alongside young midfielder Josh Benson – permitted by the league to play following the expiration of contracts on 30 June.
Sheffield United were one short on their bench but arrived at Turf Moor in fine fettle following a win over Tottenham – their first since restart – which re-ignited their hopes of a top-eight finish and a possible European place.
Their confidence didn’t looked mis-placed as the Blades made a lightning start and Nick Pope needed to be alert inside the first couple of minutes to keep out an Oli McBurnie effort with his legs after a flick from David McGoldrick had teed up his strike partner.
But the Clarets had an even better chance to take an early lead when a lovely moved opened up the visitors’ defence with Erik Pieters playing the final ball for Matej Vydra to steer an effort wide with just goalkeeper Dean Henderson to beat.
Burnley gradually played their way into the ascendency as they repeated the controlled football that had brought them back-to-back wins, former United loanee Phil Bardsley stinging the palms of Henderson whose was fortunate the rebound didn’t drop closer to the fit-again Jay Rodriguez.
The Blades countered with a clipped effort over the top from McBurnie but while they look a threat from set-pieces it was the Clarets who grabbed the half-time lead from a free-kick of their own.
Dwight McNeil, switching flanks from the right-sided berth he was given up to half time, swung the ball over and when Rodriguez flicked on, Tarkowski timed his run perfectly to slide home his second goal of the season and first on home soil since a winner against Brighton 19 months ago.
Blades boss Chris Wilder waited just 10 minutes of the second half to make a double change and try to find a way past a Burnley side which had lost only one of the last 33 Premier League games they had led at half-time.
One of those coming on, striker Billy Sharp, had scored the winner the last time United tasted success at Turf Moor 12 years ago.
But the Clarets still held firm while looking to strike on the break, making a change of their own at the second-half drinks break – when a warm beverage might have been the order of the day on a chilly and blustery afternoon – as the returning Wood replaced Vydra for his first appearance since scoring against Tottenham in Burnley’s final game before lockdown.
And it was Burnley who should have struck again with a goal that could have secured the points with 12 minutes to go.
Rodriguez’s thundering volley was again only parried by Henderson, but McNeil couldn’t capitalise as he dragged his shot wide with a hurried finish.
And a couple of minutes later the Blades were level.
The Clarets had defended their penalty area superbly - with Long again stepping up to meet the challenge as Tarkowski's central ally - but this time Ben Osborn’s floated ball in following a short corner was flicked on by Sharp for Egan to meet with a half-volley he drilled into the top corner.
Visibly hurt by that, Burnley rallied for one last push to try and find a winner and Pieters almost provided it with a superb long-range strike which Henderson pushed around a post to stop the winning run.
Burnley: Pope; Bardsley, Long, Tarkowski, Taylor; McNeil, Westwood, Brownhill, Pieters (Gudmundsson 90); Rodriguez, Vydra (Wood 68). Substitutes: Peacock-Farrell, Brady, Thompson, Dunne, Thomas, Benson, Goodridge.
Sheffield United: Henderson; Basham (Rodwell 75), Egan, Robinson (O’Connell 55); Baldock, Berge, Norwood (Sharp 55), Osborn, Stevens; McBurnie (Mousset 71), McGoldrick. Substitutes: Moore, Jagielka, Freeman, Zivkovic.
Referee: Peter Bankes