Buoyed by the support of home fans, Arsenal began brightly but it was the Germans who took the lead in the 7th minute of the match. Toni Kroos latched on to teammate Thomas Muller's cross and slotted the ball past Wojciech Szczesny.
Exactly 14 minutes later, it was Muller's turn to score. Though moments before he managed to keep out Daniel Van Buyten's header, Szcezsny could not stop the German international's shot from slamming into the roof of the net.
The first half did not witness any more goals. At the beginning of the second, the current leaders in the Bundesliga seemed to be happy with their two away goals and did not exert too much.
Jack Wilshere's pinpoint passes during this period gave Arsenal fans fresh hope. Their prayers were answered as Lukas Podolski headed in a corner in the 55th minute.
However, Bayern was not to be denied a well-deserved win. When Mario Mandzukic hit a crisp volley into the net after receiving a cross from Bayern captain Philipp Lahm in the 77th minute, it was all over bar the shouting.
Arsenal manager Arsene Wenger is well aware that they have a steep mountain to climb in the second leg at Munich. According to him, it will be "like climbing Mount Everest".
Meanwhile, Joao Moutinho helped Porto beat Malaga 1-0 at home in the other last-16 tie that was played on Tuesday.