Munich - Robert Lewandowski scored twice on his 100th European appearance to leave Bayern Munich on the verge of the last 16 after a 2-0 win over AEK on Wednesday.
Lewandowski converted a first-half penalty then volleyed home with an athletic leap after the break to leave him on 56 goals in Europe.
The victory saw Bayern claim top spot in Group E with 10 points.
Benfica's 1-1 draw at Ajax virtually assures Bayern of a place in the last 16 and a point against Benfica in three weeks will guarantee their place in the knock-out phase.
"We took a good step forwards and had the game under control in the decisive moments," said Lewandowski.
"We know that we can do better, but the win was very important for our self confidence."
The win at the Allianz Arena will ease the pressure on head coach Niko Kovac with the defending Bundesliga champions only third in the table before Saturday's showdown at leaders Borussia Dortmund.
"We deserved the win and managed to keep them scoreless," said Kovac.
"In the second half we should have rewarded our hard work with two or three goals.
"There were no fireworks out there and neither were any expected."
Kovac abandoned his experiment of playing Joshua Kimmich in the central midfield role vacated by injury to Thiago Alcantara.
The initiative had only resulted in a performance Kimmich described as his "worst in three years at Bayern" in Saturday's lacklustre league draw with Freiburg.
Instead, Javi Martinez controlled the midfield against Greek side AEK and it was a cross from Kimmich, who reverted to right-back, which led to the second goal.
Lewandowski hauled down
Bayern had a scare after five minutes when AEK defender Vasilis Lampropoulos slipped his marker, Mats Hummels, and glanced his header just wide of the post from a corner.
The hosts eventually took the lead, at the sold-out Allianz Arena in front of 70,000, when Lewandowski was pulled down by his shirt in the area.
The Poland striker sent AEK goalkeeper Vassilis Barkas the wrong way as he converted the spot-kick with half an hour gone.
However after the disappointing draw with Freiburg, this was another unimpressive display from Bayern.
The hosts were too often content to defend deep rather than go on the attack, as they tend to do on European nights at home.
They made a brighter start to the second half when Kimmich fired in a cross which Leon Goretzka volleyed straight at Barkas just before the hour mark.
The Germans then began to turn the screw.
Lewandowski had a shot saved and AEK's discipline waned as midfielder Andre Simoes and Lampropoulos both picked up yellow cards.
The hosts finally scored their second when Kimmich whipped in a corner, which was flicked on to Lewandowski, who volleyed home at the far post on 71 minutes.
There was plenty of relief at the three points won when the final whistle went, but Bayern will need to improve significantly if they are to be challenge for the title.