Stuart Gray made sure that the Clarets have still not lost successive Championship games this season as he masterminded a morale-boosting start to 2011 with victory in his first game in charge.
Burnley's caretaker manager saw his side show great character to come from behind and get themselves back onto the edge of the play-off zone with goals from Chris Eagles, Chris Iwelumo, Jay Rodriguez and substitute Steven Thompson.
It was the perfect response to the disappointment of the home defeat to Scunthorpe that ultimately spelled the end of Brian Laws' time in charge at Turf Moor.
Sheffield United were also looking for a fresh start after appointing Micky Adams as their new manager as they sought to pull away from the relegation places.
But it was the Clarets' change of direction which provided the more immediate tonic once they had recovered from the shock of falling behind to Mark Yeates' early goal.
A spectacular equaliser from Eagles steadied the ship before a quick double just before the break from top scorer Iwelumo and the irrepressible Rodriguez paved the way for a ninth home success, sealed late on by super-sub Thompson.
Gray was decisive in making four changes to his first starting line-up with one of the beneficiaries, midfielder Dean Marney, heading an early chance at goalkeeper Richard Wright in an up-tempo start.
Chris Eagles swerves home the equaliser
But the early warning signs were there with Jamie Ward breaking away and forcing Lee Grant to parry his shot as he cut in to test the Clarets' keeper.
And when the same combination squared up again with nine minutes gone it was the Blade who came out on top.
Ward's shot was saved by Grant but not cleared from the danger area and when the ball dropped at the feet of Yeates, the midfielder coolly picked his spot to find the bottom corner.
Given the week the Clarets have endured and with the pressure suddenly cranked up an extra notch, the players could have buckled. But to their credit they hit back superbly.
The return of Eagles was like a breath of fresh air, and with the winger driving forward at every opportunity and Wade Elliott enjoying an outstanding reunion with the club he denied promotion to the top flight two years ago, the Clarets always carried a threat.
A cross from Elliott saw Graham Alaxander's shot blocked and when Brian Easton returned the ball from the opposite flank Iwelumo's header was saved by Richard Wright at full stretch.
Chris Iwelumo makes it 2-1
Elliott then switched wings and pulled the ball back for Rodriguez, whose shot would surely have beaten Wright had it gone a yard either side of the grateful keeper.
The Clarets just needed a bit of magic to find a way through and with half an hour gone Eagles delivered it.
Alexander's surge forward was interrupted on the edge of the penalty area and as the ball bounced 30 yards from goal the Blades probably felt safe.
But Eagles opted to take the direct route to goal and his swerving shot was perfectly struck to deceive Wright and go in off the inside of a post.
The goal instantly lifted the mood around Turf Moor and by half-time the Clarets were seemingly cruising through calmer waters again thanks to two goals in as many minutes.
Iwelumo had been left out for the last two games but the big striker does what he does best by stretching to head home a perfectly delivered Michael Duff free-kick to move into double figures for the season.
And Rodriguez, who was battling to overrcome a bug, then got the goal he deserved in the second minute of injury time when he got on the end of an Elliott cross to drill home a left-footed shot to take his tally for the season to five.
Jay Rodriguez cracks in the third
The Clarets had got themselves just where they wanted to be, but within 40 seconds of the second half starting the game was back in the balance as United made it 3-2.
Doubtless mindful of their slip-up against Leeds United here before Christmas and at Bramall Lane in October, when the Blades came back from two goals down to pinch a point, Burnley would have wanted to have given the visitors no encouragement.
But within moments Ched Evans was tripped by Duff and the striker picked himself up to score from the penalty spot.
Inevitably the momentum swung for a spell and Leon Britton forced Grant to save following a corner. But Burnley rode out a minor storm and started to threaten themselves again as Rodriguez twice went close as Eagles and Elliott once more stretched United's defence.
At the other end, Blades' substitute Daniel Bogdanovic got a brief sight of goal as a free-kick was flicked beyond the far post. But his shot barely troubled Grant before Iwelumo put a half-chance wide with his last touch ahead of making way for Thompson as Gray made his first change in a bid to complete the job.
And it proved an inspired decision as Thompson killed the game off five minutes from time with his first league goal of the season.
And Steven Thompson makes it four
Eagles created the opening with another penetrative run and after receiving a pass from the winger just inside the penalty area, Thompson showed great composure to steady himself, hold off the closing pack of defenders and roll the ball into the corner of the net.
The impressive Tyrone Mears then had a chance to add a fifth in injury time to take Burnley into the top six on goal difference. But with the full-back shooting into the side netting that will have to wait for another day!
Burnley: Grant, Mears, Easton, Duff, Carlisle, Alexander, Marney, Elliott (Edgar 90), Rodriguez, Iwelumo (Thompson 80), Eagles. Subs: Cork, Edgar, Bikey, Guidetti, Wallace, Jensen.
Sheffield United: Wright (Simonsen ht), Calve, Nosworthy (Parrino ht), Ertl, Lowton, Yeates, Williamson (Bogdanovic 71), Britton, Cresswell, Evans, Ward. Subs: Kozluk, Bogdanovic, Slew, James, Harriott.
Booked: Williamson 71
Referee: Rob Shoebridge.