As Boris Johnson, Jeremy Corbyn, Jo Swinson and Nicola Sturgeon can testify, Sheffield is a tough place to audition for a job. None of the party leaders appeared to particularly enjoy Friday’s live pre-election debate on the BBC but if they found the South Yorkshire audience tough Ole Gunnar Solskjær endured an even more excruciating time here.

Granted, the denouement could have been worse and his tactical switch did ultimately help turn a 2-0 deficit into a 3-3 draw, but this game only strengthened Mauricio Pochettino’s candidature for potentially succeeding the Norwegian at Old Trafford.

Even by Manchester United’s standards the three goals scored by Brandon Williams, Mason Greenwood and Marcus Rashford in seven late second-half minutes to briefly put them 3-2 up were extraordinary but for much of a dank, dark, thrilling afternoon the home fans delighted in taunting Solskjær with chants of “sacked in the morning” and “are you Wednesday in disguise”?

When Oli McBurnie’s volley finally secured his side the draw that leaves them sixth, a point ahead of their ninth-placed guests, the overwhelming sense was that justice had been done.

Sir Alex Ferguson was here to monitor not just the progress of his former team but also that of Chris Wilder, a coach he once mentored as the Yorkshireman climbed his way up through the divisions.

If Sheffield United’s manager will always be grateful he was evidently determined to make Ferguson’s viewing uncomfortable and, sure enough, David de Gea was swiftly called to arms, the Spain goalkeeper making a superb double save.

First De Gea repelled John Lundstram’s high-velocity, first-time volley and then from the fallout kept David McGoldrick’s header out. McGoldrick though did aim straight at the keeper after finding himself completely unmarked.

No matter. His side had clearly identified Phil Jones as a weak left-sided link in the back three and were soon ahead. When Jones was shrugged aside – or arguably fouled – by the excellent Lys Mousset, De Gea diverted Lundstram’s shot only to see it rebound conveniently for John Fleck to redirect the ball into the net.

By now it had become abundantly apparent that Andreas Pereira is no Roy Keane and his evident discomfort as the midfield enforcer, in the injured Scott McTominay’s absence, played into Wilder’s hands. It hardly helped that Solskjær’s starting 3-4-3 formation left Pereira and Fred outnumbered in that central department, leaving Lundstram and Oliver Norwood dictating midfield.

It rendered Simon Moore almost embarrassingly under-employed in the home goal. With Dean Henderson unable to play because of the terms of his loan from Old Trafford, Moore made his first league start for 18 months but Manchester United did their very best to soothe any nerves he might have been harbouring.

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It took them half an hour to muster a shot on target, Anthony Martial dispatching the softest of scuffed efforts in Moore’s direction but at that stage a lack of attacking threat probably represented the least of Solskjær’s problems.

His players were struggling to string two passes together and, even worse, the Blades’ intelligent use of their ample possession made it an unhappy return for Harry Maguire. The England central defender began his career here but failed to show why he now commands an £80m price tag.

Something had to change and Jones was duly withdrawn at the interval, with Jesse Lingard coming off the bench as Manchester United reverted to a back four.

If the idea was to restore strength and stability it worked – although not initially. When Pereira forfeited possession, Fleck’s fine pass picked out Mousset and after the Frenchman dodged Maguire his powerful long-range shot flew low past De Gea.

Facebook Twitter Pinterest Marcus Rashford strikes to put Manchester United 3-2 up, having been 2-0 down. Photograph: Peter Powell/EPA

The ground echoed to “there’s only one United” but it was tempting fate as two teenagers and Rashford were about to launch a Mancunian rescue mission.

Williams advanced from left-back to score a wonderful first goal for the club, his devastating half volley whizzing beyond Moore after Daniel James’s cross. Tellingly, it was probably the first time James had gone past Enda Stevens.

Not to be outdone, Greenwood met Rashford’s cross, getting in between Phil Jagielka and Chris Basham to stab in the equaliser. Then James and Martial exchanged passes, with the latter cueing up Rashford to fire in an apparent winner from eight yards.

McBurnie, though, had a very different ending in mind and delighted in lifting the gloom that had suddenly enveloped Bramall Lane in a fog of despair.

Having controlled a fellow substitute Callum Robinson’s chipped cross high on his chest he volleyed the equaliser in the 90th minute, that goal surviving a VAR handball review before raising further questions about Solskjær’s job security.