BERLIN, Nov. 7 (Xinhua) -- Robert Lewandowski's brace helped Bayern Munich to a hard-earned 2-0 victory over AEK Athens in matchday four in the Champions League group stage on Wednesday.

Robert Kovac's men are on the brink of booking their berth in the knockout stages, as they sit top of Group E with a six-point advantage over third-placed Benfica and just two group matches to go.

But securing all three points on home soil was tough work for the German champions, as AEK staged a spirited performance on the road.

The Greek side nearly scored with their first chance of the game, as defender Vasilis Lampropoulos headed wide from a corner five minutes into the match. Bayern soon responded with an attack of their own, but Leon Goretzka's header from inside the box missed the target.

The Bavarians assumed control of possession as the match progressed, but they lacked the ideas to produce clear-cut goal scoring opportunities against a well-drilled AEK side.

Bayern eventually broke the deadlock in the 31st minute when Lewandowski was brought down inside the box and converted the subsequent penalty.

Into the second half, Bayern sought to pile on the pressure as Goretzka's volley and an effort from Lewandowski forced AEK keeper Vasilios Barkas into action at the hour mark.

Lewandowski remained in the thick of things as he paved the way for victory in the 71st minute. The Poland international tapped home his second of the night after capitalizing on a flicked cross from Joshua Kimmich at the far post.

With the result, Bayern top Group E with 10 points followed by Ajax (8 points), Benfica (4 points) and already eliminated AEK Athens (0 points).

"I think my team played well, just as we had hoped. We didn't just play defensively. Maybe we could have done more, but it was the first time we played like that so I'm happy with how we did," AEK head coach Marinos Ouzounidis said after the game.