In an incident-packed encounter, it was substitute Amad Diallo who sent Erik ten Hag’s side to Wembley with a strike in the dying seconds of the additional period to send the Stretford End wild, the match-winner then being sent off after getting a second yellow card for his celebrations.

It summed up everything about this thriller, United manager Ten Hag doing a dance of delight as Diallo’s shot flashed past Liverpool keeper Caoimhin Kelleher.

United desire for a place in the last four at Wembley was illustrated in a fast start which saw them take an early lead, Scott McTominay bundling home from close range in the 10th minute after Kelleher had pushed out Alejandro Garnacho’s shot.

Kelleher denied McTominay again from close range before the tie was turned on its head as Liverpool scored twice in three minutes on the stroke of half-time to take the lead and stun United.

Alexis Mac Allister equalised when his shot was deflected off Kobbie Mainoo, United paying the price for allowing the excellent Jarell Quansah to race forward unchallenged to play in Darwin Nunez.

And Mohamed Salah, the regular scourge of United, struck again swiftly with his 13th goal in 14 appearances against them, turning home in front of the Stretford End after Andre Onana saved from Nunez.

Liverpool had the better of the opportunities after the break but substitute Antony drew United level three minutes from the end of normal time with a low shot on the turn before Marcus Rashford then somehow steering a simple finish wide with the goal at his mercy to win the game.

Substitute Harvey Elliott put Liverpool back in front after 105 minutes, his 20-yard shot taking a crucial touch off substitute Christian Eriksen to swerve tantalisingly out of the reach of Onana.

It looked like the game was up for United but Rashford made amends for his earlier miss with another equaliser to set up that sensational finale with Diallo the central figure.

Huge win for Erik ten Hag

The arrival of Sir Jim Ratcliffe as United’s co-owner has increased the scrutiny, as well as the speculation, about the future of manager Ten Hag.

And while Dutchman’s position was never going to be shaped entirely by one game, there was no doubt there was a lot riding on this one against United’s arch-rivals who have been held up as the template of what they must do to get to where they want to be, enjoying the sort of success that used to be a way of life in this part of Manchester.

In the end, United pulled off a spectacular win after a game that will live long in the memory of everyone who had the pleasure to witness it.

It leaves Ten Hag with a chance of a trophy this season and the opportunity to strengthen his case to stay at Old Trafford in the new footballing structure being assembled under Ratcliffe’s rule.

The so-called “Theatre Of Dreams” has waited a long time to witness an occasion like such a raucous atmosphere, capped by wild scenes of celebration after Diallo’s winner.

United got the perfect start with McTominay’s goal but it looked like it was going wrong when Liverpool struck twice right on half-time.

Liverpool were superior in the second half but could not cash in and it was a tribute to United’s character that they stuck in to equalise through Antony three minutes from the end of normal time – and even to come back from Rashford’s horrendous miss with the final kick of the 90 minutes.

They had to climb the hill again after Elliott put Liverpool back in front in extra time but Rashford did not miss when given another opportunity, giving Diallo the chance to play the role of match-winner.

Ten Hag was beaming broadly at the end and why not? United’s fans looked like they were walking on air and their manager looked like he was about to join them.

​Liverpool pay price for complacency

Liverpool’s players slumped to the Old Trafford turf is despair as the final whistle sounded on this magnificent FA Cup quarter-final, their chances of winning a quadruple over amid the pain of defeat and wild United celebrations.

They still have the opportunity to have a truly special season as they chase the Premier League and Europa League after winning the Carabao Cup but this defeat, as well as the manner of it and who it was against, will cut deeply.

And they will know they played a large part in their own downfall, seeming to become complacent when they dominated large parts of the second half. They wasted several good situations to build on a 2-1 lead while lacking their usual urgency and cutting edge.

It left the door open for an increasingly desperate United, who were only too happy to accept the invitation against a Liverpool side who looked vulnerable when they came under threat in defence.

In a chaotic conclusion, they were caught on the counter attack when Diallo pinched possession off Elliott before leaving it to Garnacho as the Ivory Coast international made his run down the field to receive the ball back and provide the grandstand finish.

Jurgen Klopp and his players will now redouble their efforts to make it a spectacular farewell for the German manager as he prepares to leave at the end of the season but they will do so knowing they missed a big opportunity to make another Wembley appearance.