For Arsenal it was a night with heavy consequences. They gave everything but there was an air of inevitability after Wojciech Szczesny's sending-off and it will need something remarkable now to spare them from going out of the competition at this stage for the fourth year in succession.
If there is a glimmer of hope, it is that Arsène Wenger's side won 2-0 at the Allianz Arena last season. Equally it is unlikely Bayern will be as demob happy as they were that night, already 3-1 up from the first leg. Pep Guardiola's side have control of this tie, via second-half goals from Toni Kroos and Thomas Müller, and established themselves into a position of command after a night that will consume Wenger with regret.
More than anything he will look back at what happened seven minutes from the end of a chaotic first half when Szczesny left his goal-line and brought down Arjen Robben for the turning point of the match. Yet that was not the only moment to fill Wenger with anguish. Mesut Özil got it horribly wrong when he had the chance, eight minutes in, to give Arsenal a wonderful start from the penalty spot.
His attempt to beat Manuel Neuer was poor, to say the least, and he faded badly during those moments when Kroos and Philipp Lahm took control of the game. Wenger said his record signing was badly affected by the penalty but a £42.5m player should have more strength of personality and Özil's latest ordeal of a mixed season finished with Mathieu Flamini berating him after the final whistle.
The red card incensed Wenger so much he could be seen remonstrating with Robben and gesturing that it was a dive. Yet there was no doubt Szczesny had chopped down Bayern's elusive, often brilliant, wide man as he ran beyond Arsenal's line of defence after Kroos's clever up-and-under. The issue was whether it was a clear opportunity to score. Robben did not seem to have the ball under control and on that basis Arsenal were probably entitled to feel the Italian referee, Nicola Rizzoli, should have brandished only a yellow.
What followed was extraordinary, bearing in mind Özil had already demonstrated how not to take a penalty, on an occasion of this significance.
Lukasz Fabianski, replacing the unfortunate Santi Cazorla, insisted on a touch of the ball before David Alaba could take aim. With the substitution and all the recriminations, Alaba had already been waiting a full two minutes and succeeded only in skimming the outside of the post.
Even then the relief of the Arsenal crowd was interspersed with an overwhelming sense of foreboding. Bayern are formidable opponents at the best of times but, with an extra man, nobody could be surprised about the way a team of this refinement took over.
Guardiola made a key switch at half-time, moving Lahm from defence into midfield, and that had a considerable impact. Kroos took his goal brilliantly, in keeping with an outstanding performance. Robben was a constant menace and it says something about Bayern when they can bring on Müller as a substitute. Bastian Schweinsteiger did not even get off the bench.
Arsenal, in stark contrast, began the night with a 21-year-old in attack who had started only one match all season, with 11 career goals to his name. Yaya Sanogo was raw and largely ineffective on a night when Wenger insisted Olivier Giroud's absence was not a punishment for off-field issues. Sanogo was not lacking in effort but, however it is dressed up, a team with genuine aspirations of winning this competition cannot be so frail in their choices.
The other unfortunate truth for Arsenal is that, at this level, they cannot be as generous as Özil was from the penalty spot. Jack Wilshere had slipped the ball through Javi Martínez's legs and sent Özil running into the penalty area. A beautifully executed check enticed the foul from Jérôme Boateng but Özil's night swiftly unravelled. Neuer was wise to his attempt to play the ball through the middle, jutting out his right hand to deflect the shot away. Wenger commented that he could still see Özil shaking his head 10 minutes afterwards. In hindsight it would probably have been better for Arsenal if Wenger had removed him, rather than Cazorla, to bring on Fabianski.
Arsenal's disappointment was exacerbated by the fact they had set off like a side that barely cared a jot for the reputation of their opponents. They were quick to the ball, slick with their passing and, at times, they pinned Bayern back. "The first 10 to 15 minutes Arsenal played incredibly," Guardiola said. "We were lucky the best goalkeeper in the world showed his qualities." Yet nobody could have expected Arsenal to continue in that manner once they had gone a man down. Bayern, 16 points clear in the Bundesliga, have far too much about them.
The second half was brutal for Arsenal, starting off with Kroos curling a wonderful shot into the top corner from 20 yards. Lahm had set up his team-mate and, drifting in from the right, Bayern's captain also created the second, crossing for Müller to score with an expertly taken header.
Bayern should also have had a penalty after Laurent Koscielny's trip on Müller. The two sides meet again in Munich on 11 March and from here Arsenal require one of the great nights of the Wenger reign.