Bruno Fernandes scored a brace, including a brilliant second goal, to give Manchester United a crucial victory in the race for the Premier League’s top six.
On a day when rivals on that front Newcastle lost to Crystal Palace, Fernandes proved the key difference by scoring a penalty and a fine strike from 30 yards at Old Trafford.
A crucial but typically chaotic win for under-fire-manager Erik ten Hag, United sit three points above the Magpies on 53.
Three days on from making torturous work of their FA Cup semi-final triumph against Championship side Coventry, the Red Devils toiled against another side that will be playing in the second tier next term.
Under-fire Ten Hag's side twice had to come from behind against Chris Wilder's doomed Blades before Fernandes' double inspired the end of the hosts' four-match winless run in the Premier League to move them up to sixth.
The hosts had started brightly enough, having 83 per cent possession and 11 attempts before Jayden Bogle capitalised on an Andre Onana error and opened the scoring in front of a stunned Stretford End.
Harry Maguire quickly levelled against his former club, only for the Blades to go back ahead through Ben Brereton Diaz early in the second half.
Fernandes drew the hosts level from the spot as the Blades conceded a 90th goal of the season - the most ever in a 38-match Premier League season - and more were to follow.
United's skipper fired home an 81st-minute rocket from 25 yards before setting up Rasmus Hojlund to add a another four minutes later.
Ineos director of sport Dave Brailsford watched the match next to newly appointed United technical director Jason Wilcox at Old Trafford, where the hosts were again without a string of players through injury.
They made two changes from shoot-out win against Coventry and the Blades made four alterations on a night when youngster Oliver Arblaster was handed the captaincy for the first time.
Wes Foderingham was among those brought in and produced an impressive display, kicked off by brilliantly tipping over a hopeful Diogo Dalot effort from distance.
Antony was proving a nuisance and Hojlund saw a low drive denied by the Blades goalkeeper, whose opposite number was soon embarrassed.
Onana's poor first touch from makeshift centre-back Casemiro's pass was followed by a rushed, wayward attempt to find to Dalot, which was intercepted by Bogle and finished impressively by the Blades man.
It was a 35th-minute shocker that led the raucous, self-deprecating away support to poke fun at the hosts and their under-fire manager.
But soon the Blades' chants switched from winning away to drawing away as one of their own levelled, with their academy product Maguire meeting Alejandro Garnacho's cross with a glancing header at the near post.
The hosts began the second period sharply, only for Ben Osborn's cutback to be slammed home by Brereton Diaz to spark Blades delirium.
It was another gut punch but again the home side rallied.
A mixture of fine defending from Auston Trusty and Dalot's dithering prevented the full-back from getting a shot away before the Blades defender was punished for putting his hands on Maguire in the box.
Referee Michael Salisbury had whistled for a spot-kick before the ball ended up in the net, with Fernandes having to step up to smash past Foderingham.
The embattled visitors continued to threaten, with Brereton Diaz's drive ricocheting narrowly wide off Maguire before he saw a goal-bound attempt blocked.
But for all of United's problems this season, they have frequently showed an ability to dig deep in uncomfortable moments.
Fernandes epitomises that resilience and struck a thumping 25-yard drive that flew into the top corner and raised the roof in the 81st minute.
The relief was as palpable as the joy, with Hojlund striking home from close range from Fernandes' cross soon after.
With the result all but secured - even by United's recent wobbly standards - Ten Hag handed a debut to 18-year-old Ethan Wheatley, who became the 250th academy graduate to make his first team debut for the club.
