Everything that Arsenal had poured into a hugely impressive Champions League campaign came down to this. It was not about more plaudits, more pride. It was purely about taking the next step, moving to the verge of history. On an increasingly frenzied night, when the ghosts of previous near misses under Mikel Arteta provided a part of the story, they made surely the boldest advance so far under their manager.

When it was over, Arteta led the wildest of celebrations, the emotions spilling everywhere, the party set to rage long into the night. But it was the prospect of what lay ahead in the final against Paris Saint-Germain or Bayern Munich that tantalised. No club has played more European Cup or Champions League games than Arsenal without winning the trophy. Could the longest of waits be about to end?

There was suffering for Arsenal. Of course there was. It is unavoidable on nights like these and Arsenal hearts skipped beats at various points, especially when the Atlético Madrid substitute Alexander Sørloth swung at an inviting low cross in the 86th minute and missed.

Arsenal deserved to progress. They were the better team in the first half and they did enough after the interval, two certainties seeing them through. One was their bolted door defence, which has conceded only six goals in the competition, two of them coming in the meaningless final tie of the league phase against Kairat.

The other was Bukayo Saka. The winger will remember his gilt-edged miss in the semi-final second leg at PSG last season, which could have reduced the aggregate deficit to a single goal with 10 minutes still to play. There were no regrets for him here, only the glory of his decisive goal at the end of the first half – a close-range finish after the Atlético goalkeeper, Jan Oblak, had coughed up a Leandro Trossard shot.

Arsenal are into only their second final; the first since 2006 when they lost to Barcelona. They will be the underdogs against PSG or Bayern. And yet they will back themselves to spring the upset. After all, nobody has beaten them thus far in the tournament this season.

It was a night that was framed from an Arsenal point of view by the sense of possibility, partly because of what had happened on Monday night at Everton where Manchester City could only draw. Arsenal can almost touch the Premier League title. This was something else, a shot at the ultimate club final and the idea had been to harness the good vibes from Saturday’s win here against Fulham, which had been thumping and unusually stress-free.

End-of-season Fulham or Diego Simeone’s Atlético in a showpiece semi-final? Nobody in Arsenal red had anticipated anything other than a battle royale and that was how it played out.

Arsenal were on the front foot in the first half and they probed for gaps. Three times they got in behind but Atlético either cleared or locked up the middle. Everything changed when Arsenal did so for a fourth occasion in the 44th minute.

It was a pass up the inside right from William Saliba and Viktor Gyökeres was in; Oblak racing from his line, then thinking better and retreating. Gyökeres crossed and when it went all the way through for Trossard on the far side, Atlético fought to regain their shape. Trossard jinked inside and unloaded, and Oblak may have seen it late through a crowd. His parry was weak and Saka was the sharpest to the rebound.

Atlético had a couple of flickers up the right in the early running. Giuliano Simeone crossed low for Julián Alvarez, who shot wide under pressure. Then, when Antoine Griezmann pulled back, the ball broke for Simeone Jr and it needed a block tackle from Declan Rice to close him down. Rice was outstanding in a deep midfield role. Arsenal shouted for a penalty after Griezmann’s light touch on Trossard in the 35th minute. It would have been a soft one.

Atlético pushed at the start of the second half; Arsenal sitting in, looking to punch on the counter. Dressed in trademark black, Simeone prowled his technical area, living every moment, and he howled for a penalty when his son, Giuliano, fastened on to a poor back header by Saliba and went around David Raya, his first touch true. Was he nudged by the chasing Gabriel Magalhães? It was hard to tell. Simeone could not finish.

Gyökeres had a shot blocked after a Rice-led break and Atlético went close when Griezmann worked Raya. Marc Pubill was ruled to have fouled Gabriel as he chased the rebound and it was just as well for Arsenal because in the next action, Riccardo Calafiori caught Griezmann with his studs. The decision against Pubill was hard to swallow for Atlético.

Arsenal looked for the knockout blow as the game became stretched and Gyökeres nearly landed it after a cross from the substitute Piero Hincapié. Gyökeres shot first-time in front of goal but he lifted it high.

Pubill would dice with a red card with a foul on Gyökeres when he appeared to be the last defender but all that mattered to Arsenal was keeping Atlético out. After Sørloth blew his chance, Atlético would not get another.