This was the grandmother and granddaddy of all FA Cup ties which at a breathless close had Manchester United somehow scraping through 4-2 on penalties, after a beyond ­valiant Coventry City reeled in a 3-0 deficit at 71 minutes, forcing extra time in the 95th of the regulation, via Haji Wright’s cooler than cool ­equalising penalty.

When the shootout came Bradley Collins saved Casemiro’s opener before Coventry took a 2-1 lead through Wright and Victor Torp, Diogo Dalot scoring United’s. Then came sheer heartache for the Sky Blues as they failed to register again.

Related: Coventry City 3-3 Manchester United (2-4 pens): FA Cup semi-final – live reaction

After Christian Eriksen made it 2-2, André Onana dived right to save Callum O’Hare’s effort, Bruno Fernandes took United to 3-2 and, then, agonisingly, the Coventry captain, Ben Sheaf, skied his attempt. This left Rasmus Højlund to put Erik ten Hag’s embattled men into a second consecutive FA Cup final against Manchester City: he did, the strike clean and to Collins’ left.

Yet dicing with departing the competition and killing any chance of silverware after cruising against the Championship’s eighth-ranked team is a calling card Ten Hag could have done without leaving for the watching Sir Jim Ratcliffe to decide his future.

On 59 minutes the delighted United’s fans chant of “Bruno, Bruno” to their captain signalled their third and this semi-final seemingly over. But, with this Ten Hag vintage, even a three-goal lead is not enough.

Related: Erik ten Hag bemoans Manchester United’s ‘very low levels’ in FA Cup scare

In the fight to keep his job the air-punch that greeted Fernandes’s smoothly engineered left-foot finish may have carried extra feeling. Yet now the self-destruct button was pressed, with Ellis Simms’s beating of Onana a quelle surprise moment. Coventry’s striker was unmarked and the move came from a clearance headed straight back at United who failed to close down Fábio Tavares, recently on as a substitute, and whose delivery was half-volleyed in off his shin by Simms.

Boosted, Mark Robins’s men raised the spectre of their manager, perhaps, serving the death notice on Ten Hag’s tenure 34 years after his strike against Nottingham Forest in this same competition apparently saved the skin of another United manager: Alex Ferguson.

For a countless time those in red were suckerpunched via a transition. Coventry broke and when O’Hare was found by Simms the forward’s shot looped off Aaron Wan-Bissaka’s back and over the stranded Onana. That was 3-2.

United were in frantic mode, as those in sky blue flooded them, and in the last minute of added time Coventry, deservedly, squared the contest. A cross beyond Onana’s left post was stabbed at by Luis Binks, another replacement, and the ball struck Wan-Bissaka’s right arm. Robert Jones pointed to the spot, the VAR backed the referee, and Wright sent Onana the wrong way, the penalty beating the Cameroonian to his left, and so the strikes of Scott McTominay, Harry Maguire and Fernandes were cancelled out.

Comically United were now grateful for the final whistle and the extra half an hour. Their regroup consisted of having to quell the resurgent Coventry and bid to retake the lead: Fernandes went close, crashing a shot off Collins’s bar two minutes in.

United’s next foray had Maguire barreling down the left and two corners followed. Eriksen’s delivery of the second corner caused a penalty shout against Bobby Thomas but Jones was not interested.

This had become a matter of desire and stamina and Casemiro, operating as an auxiliary centre-back, showed plenty of both when chugging back to chest-block Matt Godden’s goalbound shot after the forward broke.

Robins’ spirited cadre came even closer to nirvana via two moments. First Simms – and the whole stadium – thought he entered Cup folklore after twisting and unloading a rocket but his effort smashed the underside of the bar and bounced down the wrong side of the line.

Then Torp, in the only minute of added time at the end of the 120, finished supremely at the near post but after wheeling away in ecstasy – and the Coventry fans feeling the same – Wright, correctly, was adjudged by VAR to be offside ahead of his pass to the substitute.

A leitmotif of United’s troubled season has been how open they are and this was what took them so near to the humiliation of a defeat that would not have been forgotten for an age. Example: a Fernades chip turned into Wright breaking beyond halfway and Dalot’s afterburners were needed to douse the danger.

United had opened the scoring when Alejandro Garnacho, smartly, found Dalot whose buccaneering run finished with a cross that removed Joel Latibeaudiere and Collins as a factor and had McTominay shinning home from inches.

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Regal stuff from United yet another faultline – lacking composure under pressure – soon upset Ten Hag. This was caused by McTominay upending Jake Bidwell near his area: Jones awarded a free-kick and Ten Hag jabbed temples to implore greater calm.

But, now, United roved downfield and doubled the lead. Fernandes floated in a corner and Maguire rose ahead of Thomas and headed past Collins.