The German champions looked sluggish in the first half, but a two minute spell of brilliance in the second period proved all that was needed to dispatch AEK.
Bayern dominated the first half without ever taking the final step towards scoring.
Thiago passed the ball out of play in the 26th minute when he might have played in Robert Lewandowski for a tap-in.
Serge Gnabry looked bright, and some clever footwork on the left-wing led to him having a shot into the sidenetting from a tight angle.
However, despite not shown their best play, Bayern eventually found their way into the match in the 61st minute through Javi Martinez.
Arjen Robben tried to drive a cross through a crowd of AEK players, and the ball bounced up perfectly to give Javi Martinez the chance to volley a scissor kick past Barkas.
October 23, 2018
It was a brilliantly taken goal, and it inspired Bayern to score again just two minutes later.
After a clever backheel from Gnabry, Rafinha found the time and space to pick out Robert Lewandowski, who could not miss in front of an empty net.
October 23, 2018
The double-punch killed the game, and AEK looked short on ideas as they tried to press forward to little avail.
Bayern are left top of Group E, and qualification for the last 16 looks assured. AEK, on the other hand, are bottom of the group, without a point, and it would take an unlikely string of results for them to progress.