Benfica's draw with Ajax in the group's other game means that Niko Kovac's side have opened up a two-point lead at the summit and know that a point against the Portuguese side in three weeks' time will cement their place in the last 16.
They were far from their best against Marinos Ouzounidis' side – who now have no chance of progressing – and were indebted to Lewandoswki's 31st-minute penalty and smart finish in the second half to claim all three points.
Both sides had early headed chances, Vasilios Lampropoulos flashing wide and Leon Goretzka's effort at the other end tipped over by Vasilios Barkas.
The Greeks' stubborn resistance was broken just after the half-hour mark when Uros Cosic was penalised for grabbing Lewandowski's shirt at a corner, the Poland international coolly dispatching the resulting spot-kick into Barkas' top-left corner.
Thomas Muller was denied by a superb Cosic block as the hosts failed to add to their advantage before the interval.
Barkas was called into action 10 minutes after the restart, pawing away Goretzka's volley from Joshua Kimmich's teasing cross, before spreading himself well to divert Lewandowski's one-on-one effort just after the hour.
Bayern's talismanic striker was not to be denied in the 71st minute, however, showing wonderful athleticism to hook home a deflected corner at the back post to seal maximum points for Kovac's men.
What does it mean? Pressure eases on Kovac…for now
After a poor run, four straight wins appeared to steady the Bayern ship, but that weekend draw with Freiburg plunged Bayern back into crisis mode. This routine win will keep the natives happy for now, but a clash with table-topping rivals Borussia Dortmund looms at the weekend.
Pointless AEK, meanwhile, remain rooted to the bottom of Group E and have failed to win in 24 away Champions League games. They only have faint hopes of salvaging a Europa League spot, with third-placed Benfica sitting four points clear with two games to go.
Lewandowski strikes again
Not for the first time, Lewandowski was the difference for Bayern. His two strikes take him to 32 goals for the club in the Champions League – only Muller with 42 has scored more for them in the competition.
Cosic tug proves costly
It was the slightest of grabs on Lewandowski's shirt, but enough for referee Matej Jug to point to the spot. Had he kept his hands to himself, the game might have turned out differently for the Greek champions.
Key Opta facts:
- Bayern are unbeaten in all 11 of their European matches against Greek opposition (W9 D2 L0) and they have never conceded a goal in six home matches, scoring 20 goals themselves (W5 D1 L0).
- Only Cristiano Ronaldo (53) and Lionel Messi (38) have scored more Champions League goals than Lewandowski (32) since the striker’s debut for the German giants in the competition (September 17, 2014).
- Lewandowski has scored 21 goals in the Champions League group stages since the 2014-15 season – only Messi (29) and Ronaldo (28) have more in this period.
- The Poland star has been involved in 16 goals in 15 competitive appearances for Bayern Munich this season (13 goals, three assists).
Bayern have that mouth-watering clash with Dortmund on Saturday, while AEK host Atromitos a day later in the Greek Super League. In this competition, Bayern host Benfica on November 27, the same day AEK bid to keep their hopes alive at home to Ajax.