Oliver McBurnie’s 90th-minute strike was awarded following a nervous wait as the video assistant referee reviewed the goal for a potential handball as the forward controlled Callum Robinson’s cross.
Three goals in a blistering seven minutes appeared to have rescued Solskjaer’s largely lacklustre side, who looked all but beaten after Lys Mousset added to John Fleck’s opener for Chris Wilder’s side seven minutes after the interval.
But 19-year-old left-back Brandon Williams’ goal after 72 minutes sparked the visitors into life, before substitute Mason Greenwood levelled and Marcus Rashford sent the visitors ahead.
That was not enough to see off a resilient Sheffield United, however, with Manchester United ninth in the standings after McBurnie’s late equaliser.
In a remarkable game, the Blades dominated their opponents for long periods and looked set for a first league win over Manchester United since 1992.
David de Gea had already produced fine saves to keep out John Lundstram and David McGoldrick when Mousset robbed Phil Jones in the build-up to the opener.
Mousset teed up Lundstram – whose shot was saved by De Gea before Fleck bundled home the rebound.
It went from bad to worse for Solskjaer’s side as Mousset beat De Gea with a sumptuous drilled finish from outside the penalty area.
However, the visitors turned the game on its head, as Williams produced a clever first-time finish before Greenwood scored from close range.
England forward Rashford thought he had won it 11 minutes from time after rounding off a fine move by tucking home from eight yards, only for McBurnie to level – after a lengthy check by the video assistant referee to see if the Scotland striker had handled before scoring.
Uncomfortable afternoon for Solskjaer
Manchester United had won five of their previous six games in all competitions to leave manager Solskjaer optimistic about the future after a difficult start to the season.
Yet this was an uncomfortable watch for long spells as his players were bullied by the newly promoted Blades – days after Mauricio Pochettino, linked with a move to Old Trafford last season, became available after being sacked by Tottenham Hotspur.
Despite their late comeback, United have won just one of their past 11 Premier League away games. They have also failed to keep a clean sheet in their past 12 top-flight away games, their worst streak since a run of 15 in 1985-86.
With more points dropped, Manchester United sit nine points adrift of the top four Champions League qualification spots.
They managed just one shot on target during a woeful first-half showing – Anthony Martial testing goalkeeper Simon Moore, who was making his first Premier League start, in the 29th minute.
Their second shot on target started the comeback – Williams’ shot nestling in the corner before Greenwood’s equaliser after good work by Rashford, who converted the third from Daniel James’ cut-back.
Spirited Blades battle to the end
Wilder did not know whether to laugh or cry at the final whistle after a game which provoked an incredible roller-coaster of emotions.
Despite missing first-choice keeper Dean Henderson – on loan from Manchester United and ineligible to play against them – as well as ever-present defender John Egan, the Blades turned on the style.
Mousset is proving one of the bargain buys of the season. Since joining from Bournemouth for £10m in the summer, the French forward has four Premier League goals and three assists.
He was heavily involved in his side’s first before producing a sublime finish to double the lead.
Wilder will be concerned at the way his defence capitulated but Sheffield United’s never-say-die spirit was once again evident.
This was the fifth time this season they have come from behind to salvage a point in the Premier League.
Man of the match – Lys Mousset (Sheffield United)
Man Utd dangerous when two-goals down – the stats
- Manchester United have avoided defeat in 25 Premier League games when losing by two or more goals – three more than any other side.
- This was the highest-scoring Premier League draw involving Manchester United since January 2016, when they drew 3-3 with Newcastle United.
- Sheffield United are the first newly promoted team to score three goals against Manchester United in a Premier League game since Leicester City won 5-3 in September 2014.
- In Brandon Williams and Mason Greenwood, Manchester United had two teenagers score in a Premier League match for the first time since Wayne Rooney and Giuseppe Rossi scored against Sunderland in October 2005.
- Sheffield United have benefited from more goals (five) from substitutes in the Premier League this season than any other side.
- Manchester United striker Marcus Rashford has been involved in eight goals in his past five Premier League appearances against newly promoted opponents.
- Phil Jagielka made his first Premier League start for Sheffield United since May 2007, a gap of 4,578 days. The only player to have a longer gap between starts for a club is Wayne Rooney for Everton between 2004 and 2017 (4,837 days).