Arsenal faced an uphill task to stop the German Giants to fight again for the European Glory after losing to Chelsea last season in Final, who comfortably beat Arsenal 3-1.
The hosts started off with a thundering goal from Kroos, Thomas Mueller doubled the lead for the Germans and misery for the Gunners.
Lukas Podolski led the recovery when he nodded in Jack Wilshere’s corner before Olivier Giroud had a shot saved.
But Mario Mandzukic restored the two-goal cushion by tucking in late on.
Bayern’s passing and movement was, at times, far superior, and Arsenal face an uphill struggle in the second leg with the German side losing just once at home this season.