Chris Wilder's men, fighting for their lives at the bottom of the table, surprisingly led twice at the Theatre of Dreams, with Jayden Bogle and Ben Brereton Diaz netting either side of half time.
After Wes Foderingham made a plethora of crucial saves in the first half, Brereton Diaz fired home his goal from close range five minutes after the interval to give the travelling Blades supporters hope of seeing their side end a nine-game winless run.
However, Harry Maguire - who scored an equaliser in the first half against his former club - won a penalty for Man United on the hour mark, and Bruno Fernandes stepped up to convert from 12 yards before contributing to another two goals in the closing stages to complete the turnaround.
Fernandes fired a stunning 25-yard strike into the top corner to put the Red Devils ahead with just nine minutes remaining, shortly before setting up Rasmus Hojlund to secure victory for the hosts, condemning the Blades to their 24th league defeat of the season.
Sheffield United make unwanted Premier League history
Sheffield United's spirited display at Old Trafford was ultimately in vain and they were made to rue more defensive errors as they cling onto their Premier League survival hopes by the finest of threads.
The Blades have now conceded four or more goals in eight Premier League games this season, more than any other team in the division.
In total, Wilder's side have shipped 92 goals across their 34 matches, the most ever conceded in a 38-game season in the competition, surpassing the previous record held by Derby County (89) in 2007-08.
With four games still remaining, Sheffield United are in contention to break the all-time Premier League goals against record held by Swindon Town, who conceded 100 goals during a 42-match campaign in 1993-94.
The Blades, who remain rooted to the foot of the table and 10 points adrift of safety, will be relegated to the Championship if they lose at Newcastle United on Saturday. Even if they were to draw or win against the Magpies, who thrashed them 8-0 in the reverse fixture, relegation will be confirmed if 17th-placed Nottingham Forest match or better their result when they host Manchester City on Sunday.
Wilder bemoans Sheffield United's defensive fragility
Asked if he can take pride from Sheffield United's performance following another defeat, Wilder said at his post-match press conference: "I'm a bit bored about saying that. There's been times when we've been exposed so we have to accept it and take responsibility.
"It's bittersweet, coming here in front of 75,000. I don't go with the narrative Man United are poor, you've got world-class players all over the park. You look at one teamsheet and the other teamsheet, that's the best team we can put out, and you expect to be under pressure and your goalkeeper to make some saves, which he did, which is great because he's a good pro.
"We scored two away from home to take the game deep, they're positives. The negatives yet again is if we make better decisions from a defensive point of view we come away with more, like we should have done with so many more points than we've got in my time here.
"That's the disappointing thing, the ball goes in the back of our net far too easily. Just as they find the big moments, there's an art to defending as well. It's both penalty areas and we yet again have been not great in terms of the goals that have gone in."
After travelling to St James' Park on Saturday, Sheffield United will conclude the season with fixtures against Nottingham Forest, Everton and Tottenham Hotspur.