The Blades looked set to secure only their second point of the season when Oli McBurnie scored his first of the campaign after Ayoze Perez had given the visitors the lead.
But with just a few minutes of the match remaining, James Maddison fed in striker Jamie Vardy, who scampered clear of the home defence and slotted his shot past Aaron Ramsdale.
The 33-year-old boyhood fan of Blades’ rivals Sheffield Wednesday celebrated by running to the corner flag and snapping it with his boot.
United, who have made the worst start by any club to a Premier League season, now only have one point from 11 games and sit five points adrift at the bottom.
“If players want to stay in this division then they have to make better decisions,” Wilder told BBC Radio 5 Live, referring to the errors made by Chris Basham and John Fleck in the build-up to Vardy’s late goal.
“We’re all worried because we care about results and performances. We’re in this position for a reason.”
Wilder, who has led the Yorkshire side to two promotions, added: “We are a losing team at the moment and I am the manager of a losing team.
“Whether it is cruel or deserved, we have to make the right decisions. If we make the right decisions we get something from the game against a really decent team.”
Earlier, Vardy and Maddison both came close with fierce efforts that struck the Blades’ right-hand upright.
Oliver Burke had United’s only other chance of note when he slipped with just Kasper Schmeichel to beat.
Blades’ situation becoming critical
Last season must have seemed like a dream to some Blades supporters.
Chris Wilder’s men were among the European places for much of their first campaign back in the top flight before falling away in the home straight. However, few would have thought those tail-end results would be the first symptoms of ‘second-season syndrome’.
United still remain difficult to beat, having only twice lost by more than one goal in the league this season but it is at the other end where they have suffered – it was only four goals in 10 games with a conversion rate of 4.2% before Sunday’s game.
So when Burke fluffed his lines with just Schmeichel to beat midway through the first half, it seemed like Groundhog Day for the home side; the feeling exacerbated when Perez thrashed in the Foxes’ opener.
Spirits were lifted when McBurnie equalised soon after from a corner for his first in the competition in 15 appearances and after 20 efforts on goal. However, instead of building on that, the Blades reverted to type by focusing on soaking up pressure from their opponents.
Just when they thought Brendan Rodgers’ cavalier side had thrown everything at them, they were undone by the flashing blade that is Vardy.
It is now one point from a possible 33. Wilder has produced near miracles at the clubs he has managed, but surely this situation is impossible to turn around?
Fresh Vardy helps Foxes to victory
Leicester will no doubt be glad for the respite from their Europa League-Premier League schedule that will follow their match at home to AEK Athens this Thursday.
However, unlike Burnley, whose form suffered when they tried to cope with their European experience in 2018-19, the Foxes have enough depth in their squad to field two strong XIs.
Leading hitman Vardy was one of the four senior players left out from the 4,000-mile round trip to Ukraine last week to face Zorya Luhansk, and his team benefitted from his freshness at Bramall Lane.
The forward was very unlucky not to score in the 10th minute as his strike thundered off the Blades’ left-hand upright, but his fizz never fell flat and there was only one winner when he raced clear to clip in the winning goal.
His unpredictable movement had the Blades constantly guessing as did that of Perez, who was in the perfect spot to smash home the opener after Marc Albrighton’s initial effort was blocked. Maddison also impressed in midfield and, like Vardy, saw his great strike rebound off the post before providing the assist for the winner.
The one negative for Rodgers was that his side’s Achilles flared up again when for the eighth time this season they conceded from a set-piece.
‘There’s not too many better than Vardy’ – reaction
Leicester City manager Brendan Rodgers, speaking to BBC Sport: “The mark of how you’re judged as a team is how you bounce back.
“We showed confidence and it was a case of at half-time reinforcing a few things and perseverance. We scored a good first goal, defended when needed and it was a great second goal for us and a deserved win.
“James [Maddison] has great vision, he sees a pass so early and he has a relationship with Jamie [Vardy] on the pitch. Jamie, once he’s away in that position, there’s not too many better.”
Burke’s unlucky run continues – stats
- United have become just the ninth different team in English Football League history to lose 10 (or more) of their first 11 league matches of a season, and only the third in the top flight after Newcastle in 1977-78 and Manchester United in 1930-31.
- Only Liverpool (19) and Manchester City (18) have won more Premier League away games than the Foxes since Brendan Rodgers took charge of Leicester (14).
- Leicester have conceded more Premier League goals via corners this season (six) than they did through the entire 2019-20 campaign (five).
- United’s Oliver Burke has now appeared in 21 Premier League matches without winning any (D3 L18); from the start of a player’s Premier League career, only Gareth Bale (24), Nicky Summerbee (23), Craig Fagan (23) and Giles Barnes (22) appeared in more matches before winning for the very first time in the competition.
- Maddison has provided his first Premier League assist in 363 days, since doing so against Aston Villa in December last year (56th created chance since).
- McBurnie has scored more of Sheffield United’s 44 Premier League goals since they were promoted last season than any other player, with six of his seven goals coming at Bramall Lane.
Leicester face AEK Athens in their final Europa League group match on Thursday (20:00 GMT) before they host Brighton in the Premier League on Sunday (19:15). United are at Southampton next Sunday (12:00).