Jack Harrison gave the Whites an early lead before Ben Osborn equalised on the stroke of half-time.
Phil Jagielka then put the ball into his own net after the interval to hand Marcelo Bielsa’s all three points.
As for the Blades, they now find themselves 15 points adrift of safety with eight games left to play.
We’ve taken a look back at that game, and some of the other major talking points from this weekend’s action, below:
Rodrigo makes 'sleeping' Leeds United admission and declares action plan after Whites punishment
Leeds United in ‘talks’ with MLS star as Man Utd eye deal for Whites goalkeeper
Leeds United ‘would have taken’ four points from two games according to Alan Shearer
Defiant Ralph Hasenhuttl offers Leeds United apology after Southampton score draw
What is happening to former Leeds United star Raphinha at Barcelona amid latest farce and deadline
Chelsea 2-5 West Brom: Big Sam stirs from hibernation
Sam Allardyce is inevitable.
The Premier League’s most fabled firefighter has never been relegated from the top flight, despite taking on some precarious gigs, to put it diplomatically.
For all the world it looked as if West Brom would be the club end Big Sam’s charmed run at the top table of English football, and the likelihood is that they still will be, but Saturday’s pulsating victory over Chelsea at Stamford Bridge may well have given the Baggies a fighting chance at a great escape.
It was a performance that had all the hallmarks of those galvanising catalysts that have punctuated Allardyce’s career to date, and while the odds are still stacked against them, it would be foolish to write Albion off just yet.
Leeds United 2-1 Sheffield United: Harrison shines in Yorkshire derby
Much of the rhetoric at Elland Road this season has centred around the impact that Patrick Bamford and Raphinha have had on Leeds United’s long-awaited return to the top flight.
The pair have both been in blistering form at times, and put in eye-catching performances again against the Blades, but it was Harrison who ultimately made a couple of crucial contributions.
The winger tapped in from point blank range to give his side an early lead, and might have had a second were it not for a smart save from Aaron Ramsdale.
After the interval, it was Harrison who delivered the wicked cross that forced Phil Jagielka to skew the ball into his own net to hand Leeds all three points, and to keep them in the running for a top-half finish.
As for Sheffield United, if Paul Heckingbottom keeps them up from here they should name all four stands at Bramall Lane after him.
Arsenal 0-3 Liverpool: Things starting to click for disjointed champions
In terms of this season, the horse has long bolted on Liverpool’s title challenge, but there is still plenty to play for at Anfield.
A top four finish is a must for the Reds, and they’re still very much alive and kicking in the Champions League.
What a relief it will be for Jurgen Klopp, therefore, to see his side finally look a little more like their old selves against Arsenal at the weekend.
His side were dominant against the Gunners, and they largely had midfield duo Fabinho and Thiago to thank for their improved display.
It’s amazing what a team can do when they’re able to play their most talented players in the correct positions.
Southampton 3-2 Burnley: Saints arrest slump in nick of time
Southampton have been plummeting like a cartoon anvil in recent months, and as this Premier League season continues to twist and turn, there was a growing feeling that the Saints could have been dragged down into a relegation battle.
Two wins out of three, including a 3-2 comeback against Burnley at the weekend, have helped them to ease some of those fears, however, and with a 10 point gap between themselves and the relegation zone, you would fancy them to be safe from here.
As for Burnley, the buffer is seven points.
That cushion should be enough for Sean Dyche's men, but a win on Sunday would have significantly helped their situation.
Newcastle United 2-2 Tottenham: Toon cause Spurs real problems
In a plot twist that M. Night Shyamalan himself would have been proud of, Newcastle United – darlings of drudgery – actually looked dangerous against Tottenham on Sunday.
In fact, the Magpies recorded an xG of 4.3 against Jose Mourinho's men – the third-highest tally of any club in the Premier League this season.
Alas, it wasn’t enough to secure all three points, but were it not for some absurd goalkeeping heroics from Hugo Lloris, things perhaps could have been very different.
With Fulham losing against Aston Villa, could this be the boost that Newcastle need to pull clear of danger?
Fulham 1-3 Aston Villa: Cottagers beginning to drift
Newcastle's result was always going to be viewed through the prism of how well Fulham got on against Aston Villa, and when former Toon striker Aleksandar Mitrovic gave Scott Parker’s men the lead midway through the second half, there must have been a run on bed sheets, spray paint, and cabbages in the north east.
Thankfully for Newcastle, however, the Cottagers – like a dog walker who are bad at their job – are having real issues hanging onto leads at the moment, and again they let an advantage slip against the Villans.
It’s now three losses on the bounce for Fulham, and they need to rekindle some assertiveness if they are to beat the drop this term.
Manchester United 2-1 Brighton: Seagulls robbed?
Brighton arguably have every right to feel more than a little aggrieved following their 2-1 defeat to Manchester United at Old Trafford on Sunday evening.
Having taken the lead, Albion were pegged back before Harry Maguire quite clearly upended Danny Welbeck in the box with all the grace and poise of a runaway shopping trolley clattering into a display pyramid of tinned tomatoes.
How VAR deduced that there was no offence to answer for is anybody’s guess, and the baffling decision was made all the more galling by Mason Greenwood’s late winner shortly after.