A powerful Bayern side full of quality players were simply too good for Arsene Wenger's Gunners, who at stages looked like boys against men, and have now seen their Champions League hopes dashed.
The opening goal came in just the seventh minute when Toni Kroos hit a stunning first-time shot from Thomas Muller's rightwing cross straight into the ground to see it fly past a helpless Wojciech Szczesny.
Less than 15 minutes later and Bayern were two to the good when Muller was on hand to acrobatically flash home from close range after Szczesny had kept out Daniel van Buyten's close range header.
Olivier Giroud had a great chance to level the tie in the 72nd minute but his first-time side-footer was struck straight at Neuer before Bayern killed the game in fortuitous circumstances when Philipp Lahm's low cross form the right struck the foot of Mario Mandzukic before bobbling up over Szczesny and into the back of the net.
The first leg result makes it an extremely difficult task for Wenger's men in the return bout at the Allianz Arena on March 13, especially considering Jupp Heynckes' side has been beaten at home just once this season in all competitions.
2012/13 UEFA Champions League - Round of 16 first leg
Emirates Stadium, London - 59,974