Two first-half goals from Toni Kroos and Thomas Müller set them on the road to success, and while ex-Bayern boy Lukas Podolski pulled one back, the Bundesliga's leading marksman Mario Mandzukic struck to ensure Bayern went home with three away goals to their name.
Amazingly, Bayern hadn't conceded a goal since 14 December 2012, but the Bundesliga leaders were looking aberrantly vulnerable early on. Keen to venture forward in support of Franck Ribery, David Alaba was twice caught out of position and was rather fortunate to see Santi Cazorla's right-wing cross flick off Bastian Schweinsteiger and into the grateful arms of Manuel Neuer.
The Bavarians didn't get to where they are atop the Bundesliga table by accident, though, and nipping that momentary London storm in the bud, took an emphatic lead. Müller's miscued cross fell perfectly for Kroos, who lashed the sweetest of volleys beyond the reach of Arsenal goalkeeper Wojciech Szczesny from the edge of the area.
It was the perfect start for Jupp Heynckes' men, whose incisive passing was a beauty to behold for the travelling faithful. Sure enough, with just 21 minutes on the clock, the visitors stretched their lead. Daniel van Buyten was allowed a free run at Kroos' floated corner and, with Szczesny unable to keep hold of the Belgian's bullet header, Müller swept home for 2-0.
Ironic chants of "football's coming home" began to emanate from the now buzzing pockets of Bayern supporters dotted around the Emirates Stadium: Arsenal were being outplayed by one of Europe's best, and they knew it. The Gunners inevitably flooded forward, but it was yet another elegant Bayern move that almost produced the next goal as Mandzukic headed wide from Philipp Lahm.
No man's land
Bayern had done everything right, but a rare mix-up in the backline handed Arsenal an almighty lifeline ten minutes into the second half. Neuer was caught wanting from a Jack Wilshere corner, allowing Podolski to loop a routine header into the gaping net. It was the first goal the Reds had conceded in 664 minutes of football and after Kroos stung the palms of Szczesny, Heynckes deemed it prime time to introduce Arjen Robben.
The move did little to stifle the Arsenal artillery as substitute Olivier Giroud smashed a vicious volley straight at Neuer; a pivotal moment in the contest, swiftly followed by a third Bayern goal. Lahm did the hard work, racing away and crossing for Mandzukic to bundle over the line and reassert the Bavarian giants' hold on the tie ahead of the return leg in three weeks' time.
Arsenal: Szczesny - Sagna, Mertesacker, Koscielny, Vermaelen - Wilshere, Arteta, Ramsey (Rosicky 70'), Santi Cazorla - Podolski (Giroud 71'), Walcott
Bayern: Neuer - Lahm, van Buyten, Dante, Alaba - Javi Martinez, Schweinsteiger - T. Müller, Kroos (Gustavo 72'), Ribery (Robben 61') - Mandzukic (Gomez 77')
Goals: 0-1 Kroos (7'), 0-2 Müller (21'), 1-2 Podolski (55'), 1-3 Mandzukic (77')