Lewandowski's goal, his 21st in 17 games this season, was the highlight of a dull encounter at the Allianz Arena before substitute Ivan Perisic added a late second.
The victory ensures Group B leaders Bayern reach the knockout stage for the 12th straight season.
"We defended very high, put the opponent under pressure again and again and were dominant," said interim coach Hansi Flick.
The 54-year-old Flick got off to a winning start having stepped in after Niko Kovac was sacked as head coach on Sunday following a 5-1 drubbing at Eintracht Frankfurt in the Bundesliga.
Bayern expect to name a new boss by their next away game at Fortuna Duesseldorf on November 23, but Ajax coach Erik ten Hag and Paris Saint-Germain boss Thomas Tuchel have already ruled themselves out.
According to German daily Bild, Bayern are in talks with former Arsenal coach Arsene Wenger, who was evasive when asked directly about the Bayern vacancy by beIN Sports on Tuesday.
In the wake of Kovac's sacking, sporting director Hasan Salihamidzic called for a "positive" display, but Bayern's stars struggled to deliver.
"It was a hard win, we weren't rewarded enough for our work, and when we were, it was late," said Thomas Mueller after both goals came in the final half an hour.
"We were dominant and aggressive, we did what we had done in training, we didn't let them breathe, but we didn't take enough advantage of our pressing.
"I can't say I'm relieved, just happy to have won at home by being dominant."
Coutinho dropped
Flick, Germany's assistant coach when they won the 2014 World Cup, made two key changes by dropping Thiago Alcantara and Philippe Coutinho, both of whom were poor at Frankfurt.
Leon Goretzka took Alcantara's place in midfield, with Mueller replacing Coutinho and Javi Martinez playing at centre-back instead of Jerome Boateng, who was sent off against Eintracht.
Just a month ago, Bayern trounced Tottenham 7-2 in north London with Serge Gnabry scoring four goals, but the German champions could not match that display.
Their first clear chance came when winger Kingsley Coman cut inside with 33 minutes gone, but fired at Olympiakos goalkeeper Jose Sa.
The 'keeper then denied Mueller moments later, while right-back Benjamin Pavard headed off the post on the stroke of half-time.
Bayern had a better start to the second half as Goretzka's header forced Sa into a good save.
Lewandowski broke the deadlock on 69 minutes when he flicked Kingsley Coman's low cross past Sa.
The second goal was created by two second-half substitutes as Corentin Tolisso's ball found its way to Perisic, who lashed the ball into the net.