Mikel Arteta had told Arsenal to write a history of their own against an old nemesis who had done it all before and, while this was not quite a night for the ages, his ­players proved a point. They showed them­selves ­capable of facing down ­Bayern Munich as equals and on this ­evidence it will take a brave onlooker to predict the outcome of the second leg in Bavaria next week.

The result was fair, both sides convincing in some spells and looking alarmingly naive in others. Reports of Bayern’s demise have evidently been exaggerated; Arsenal, though, matched them blow for blow and put distance between the days when this fixture would routinely leave them ripe for a thrashing.

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The ­satisfaction of that will surely sink in but they departed raging with a sense of injustice, Bukayo Saka ­having to be ushered away from the referee Glenn Nyberg.

In the game’s final action Saka had burst through and knocked the ball to the side of Manuel Neuer, tumbling over the goalkeeper’s right leg. Nyberg was not interested and nor, evidently, was the lighter-touch version of VAR that generally presides over Champions League affairs. They have certainly been given before but on balance it seemed Saka had flown into Neuer and invited contact; it was a bold and perhaps defining call but seemingly the correct one.

If Arteta’s players do nurse regrets they should stem from a 20‑minute spell when, after swamping Bayern early on and richly deserving Saka’s brilliant opener, Arsenal fell back into habits that briefly brought to mind those 5-1 humiliations of yore. The mix‑up between Gabriel ­Magalhães and David Raya that sowed the seed for Serge Gnabry’s equaliser came from nowhere; the ­defending that let Leroy Sané win a penalty ­converted by Harry Kane, who was never going to let his own evening pass quietly, was abject and for a time Bayern looked capable of putting ­pro­ceedings to bed.

Perhaps the recovery tackle by Ben White on Sané, who had streaked clear in the 36th minute and saw a chance to put Bayern 3-1 up, will go down as the moment Arsenal stayed in the tie. But the bigger picture is that they showed guts to regain a foothold and turn the tide; Arteta knew he had firepower on the bench if ideas ran dry and two substitutes provided the spark that earned parity.

Gabriel Jesus would have been disappointed not to start, his ­compatriot Gabriel Martinelli preferred on the left while Kai Havertz took his now customary berth up front, but showed his capacity to make a difference with footwork that outfoxed Matthijs de Ligt and Leon Goretzka. His lay-off to Leandro Trossard, who had entered the fray with him nine minutes previously, was timed perfectly and the Belgian’s low first-time finish was too good for Manuel Neuer.

It reignited a crowd that had been cranked to fever pitch at the beginning, steeped in the knowledge that this was Arsenal’s biggest European occasion here for 14 years. They booed Kane’s every touch from the start and mocked Eric Dier given the slightest encouragement; they roared as their players snapped into a ­Bayern team who bore hallmarks of the slipshod defending that has marked their Bundesliga campaign. Within 10 ­minutes Martinelli had come close and Alphonso Davies, with a rash tackle on Saka, had ruled himself out of the second leg with a booking.

Saka’s goal came after Arsenal had hunted Bayern down deep on the right flank, White eventually playing a smart infield pass that his colleague let run across him before whipping around Neuer.

The roof lifted off a venue filled only with home fans due to a one-match ban for Bayern’s travelling support; the lead should have been doubled when White shot at Neuer after Havertz sent him through, but Arsenal were rattling away at such a tempo that more ­openings seemed certain.

Related: Arsenal still have demons and Bayern show they will not be slain easily | Jonathan Wilson

Bayern had been smothered but Gabriel, spooked by Raya’s advance 45 yards up the pitch as he retrieved possession in his own half, aimed a vague pass towards Jakub Kiwior and Bayern pounced. Serge Gnabry was set free via sharp approach play from Sané and Leon Goretzka, ­scoring confidently against his old club, and worse followed after the half‑hour. Sané was allowed to scythe from halfway into Arsenal’s box, via a missed tackle from Jorginho and an aborted one from Gabriel, before finally being felled by William Saliba. Kane took evident pleasure in rolling the penalty past Raya to eerie silence.

Arteta swapped the struggling Kiwior for Oleksandr Zinchenko but it was Bayern, brisk on the counter, who looked marginally likelier to score before Trossard’s flourish. Thomas Tuchel could rue Kingsley Coman’s late shot against the post and had his own excuse to rage when, in a bizarre 66th-minute incident, Gabriel picked up the ball after Raya had seemingly played a goal‑kick to him. Perhaps both sides’ grievances ultimately cancelled each other out; there had been little to separate them in any department here.