Once again, Joshua Zirkzee had the Manchester United fans cheering. It was his substitution they celebrated 13 days earlier against Newcastle, the Dutchman suddenly the scapegoat for a dozen years of underachievement and hundreds of millions wasted in transfer-market mistakes. But it was Zirkzee who slotted in the spot kick that eliminated Arsenal from the FA Cup, the substitute who decided a shootout. It has been an eventful fortnight for the striker; first humiliated, now feted. “Life has these beautiful things,” said Ruben Amorim.

From an ugliness, there is a beauty for United as well. From the low of Newcastle, Amorim has constructed twin triumphs of sorts. Neither a victory in 90 minutes, nor this in 120, but a draw at Anfield was followed by a demonstration of determination at the Emirates. Amorim’s reign is barely two months old and defeats outnumber wins but he has had a hat-trick of defining away games to savour: a Manchester derby, a trip to Liverpool, his second visit to Arsenal.

A fourth-round reunion with Ruud van Nistelrooy was secured by the understudies, the second-choice goalkeeper and the reserve striker. Perhaps that is fitting: there is little pretence this squad is ideal for Amorim, so he has to make the best of what he has. The greatest FA Cup tie between United and Arsenal turned on a superb penalty save, Peter Schmeichel denying Dennis Bergkamp in the 1999 semi-final. A quarter of a century on, Altay Bayindir had not one Schmeichel moment but two, saving from Martin Odegaard in the match and Kai Havertz in the shootout.

In the process, he may have spared Amorim an awkward question or two. Bayindir’s previous outing was in north London, in a knockout tie. He conceded straight from a corner as Tottenham dumped United out of the Carabao Cup, closing off one path to silverware. Amorim duly picked the Turkey international anyway, displaying a confidence in him that Erik ten Hag appeared to lack. Rewind a year and Andre Onana delayed his departure to the African Cup of Nations to play at League One Wigan, seemingly with Ten Hag’s encouragement. The sense was that Bayindir was bought by the former football director John Murtough, not Ten Hag. In the two saves Bayindir made from Declan Rice, let alone his heroics from 12 yards, Murtough may be vindicated.

It was, though, a day for Amorim. He has had no scope to change his squad yet – though Juventus’ attempts to take Zirkzee on loan feel more remote after his cathartic cameo – but he has looked to change the mentality as well, almost infamously, as the tactics.

If nothing else, he showed he could alter his trademark 3-4-3 formation, if only because he had to when he had a reduced complement of players. After Diogo Dalot’s dismissal, United were reconfigured into a 5-4-0 system. It became a 120-minute epic, of rancour and resistance. United lost their cool and then regained it. They were down to 10 men; perhaps it might have been nine, given the possibility Manuel Ugarte headbutted Kai Havertz; there was no VAR to take a second look. As it was, United had six yellow cards after 70 minutes, two of them for Dalot, but collected no more. Bruno Fernandes’ red card at Wolves brought a descent into defeat. After Dalot departed, there was no repeat.

United had a common cause, a resolve. There was some old-fashioned, backs-to-the-wall defending. Matthijs de Ligt had his finest two hours in a United shirt, a clearance from under his own crossbar his most precious intervention. Arsenal found the middle of Harry Maguire’s sizeable forehead with some of their torrent of crosses, the former captain looking ever more of a cussed Yorkshireman with each obdurate intervention. Bayindir was partly culpable for Gabriel Magalhaes’ leveller but experienced his own redemption.

He was aided by Arsenal, by Havertz’s second remarkable miss in five days and home setbacks that may have expelled Arsenal from both cup competitions. Deftly flicking the ball over the bar from four yards would be an achievement were it the aim. But there was a broader problem. Mikel Arteta’s team ended with 26 shots, 55 touches inside the United box and 42 crosses, yet they displayed too little genuine invention.

United played like underdogs; as the team 13th in the Premier League they were, even before Dalot departed. Their low block suited Maguire. Their goal came from the counter-attack, their best formula under both Ten Hag and Ole Gunnar Solskjaer, and was curled in by Fernandes, arguably their best player under each. United prevailed against the odds, just as they did in Ten Hag’s valedictory FA Cup tie, last season’s final. That was an upset that enabled him to keep his job. Maybe it proved counter-productive for United. Ten Hag somehow boxed himself into a corner by claiming a season with a trophy was a success, no matter what else went wrong. Amorim will not be fooled as easily. But Ten Hag had a wretched record away against the top clubs. So for Amorim, this was progress, and not merely in the FA Cup.