The Bundesliga side struggled to find cracks in Olympiacos' defense before Robert Lewandowski broke the deadlock in the second half with his sixth goal of the tournament, securing Bayern's place in the last 16.
The Polish forward has now scored 20 goals in 14 games this season between the Champions League and Bundesliga.
Substitute Ivan Perisic provided an insurance goal just before the final whistle. Bayern have now qualified for the knockout stage of the competition in 12 straight seasons.
Bayern haven't won the Champions League since beating Bundesliga rival Borussia Dortmund in 2013.
Wednesday's match was Bayern Munich's first under interim manager Hansi Flick, who took charge of the club following Niko Kovac's departure on Sunday. Kovac was relieved of his duties a day after Bayern fell 5-1 to Eintracht Frankfurt.