The Gunners came to Germany full of confidence and with history on their side having never lost at the Allianz Arena, but they were second-best throughout as Bayern showed that defeat at the Emirates Stadium a fortnight ago was the merest blip in their superb start to the season.
Robert Lewandowski put the hosts ahead early on as he sprung the rustiest of offside traps before a Thomas Muller brace as well as goals from David Alaba and substitute Arjen Robben did further damage — with Olivier Giroud scoring a scant consolation as Bayern ran out 5-1 winners.
Arsenal defender Per Mertesacker said: “They scored too early for us and got into their rhythm — that was too difficult for us to go again.
“It was disappointing from our point of view but because they scored early, they got into their rhythm.”
Gunners boss Arsene Wenger added: “You have to give credit to Bayern for their quality but we made things easy for them. We were extremely poor defensively.”
This galling defeat is the third in four Group F games and Arsenal are now six points off second spot with two games remaining.
However, Mertesacker still retains hope of a great escape.
“We have to win both games and get two goals on Olympiakos, but it’s not over and that’s how we have to approach it. We need to bounce back and put away negative energy.”
Mesut Ozil thought he had levelled for the visitors but was instead cautioned for handball as he turned home a Nacho Monreal cross almost straight after Bayern has gone in front.
Just 10 minutes in and Arsenal afforded Thiago the freedom of Munich as the Spain international delivered a sumptuous cross to Lewandowski, who headed home his 18th goal of the season as Gabriel played him onside.
The Brazilian, playing as Laurent Koscielny sat on the bench as a precaution due to a hip problem, had dropped deeper than his fellow defenders to play Lewandowski onside and then committed the cardinal sin of stepping up too late — allowing the Pole to open the scoring.
Ozil was away celebrating an equaliser almost straight from the restart but the German was booked as referee Gianluca Rocchi correctly ruled he used his elbow to turn home Monreal’s cross.
Bayern then had two good chances to double their advantage but Cech was on hand to keep out Lewandowski on two occasions as the hosts built up a head of steam.
The second goal followed soon after as Philipp Lahm’s cross was missed by Mathieu Debuchy, allowing Kingsley Coman to fire goalwards.
Muller was on hand to control the Juventus loanee’s shot and turn past Cech with the help of a deflection off Mertesacker’s shin.
Cech then made a superb stop as he tipped Muller’s header over the bar but, having done his best to keep his side in the game, he could only get his fingertips to Alaba’s shot as the full-back skipped past Santi Cazorla before lashing home the third just before half-time.
Pep Guardiola had resisted the temptation to play Robben despite the Holland international playing a full 90 minutes at the weekend — but he needed just one touch to add the fourth having come on for the impressive Coman nine minutes after the break.
Cazorla should have pulled one back having been played through by Giroud but shot straight at Manuel Neuer.
The Frenchman did much better with his own chance, controlling Sanchez’s chipped cross and acrobatically volleying a consolation for Arsenal.
Robben should have added a fifth after rounding Cech but dawdled and was well challenged by a backtracking Gabriel but Muller made no mistake in slotting home his second of the evening in the dying minutes to make this Arsenal’s worst-ever Champions League defeat.
Neuer, Lahm, Boateng (Benatia 68), Javi Martinez, Alaba, Alonso, Coman (Robben 54), Muller, Thiago, Douglas Costa, Lewandowski (Vidal 71).
Cech, Debuchy, Mertesacker, Gabriel, Monreal, Coquelin, Cazorla (Chambers 87), Campbell (Gibbs 58), Ozil, Sanchez, Giroud (Iwobi 84).
Gianluca Rocchi (Italy).