First-half goals from Douglas Costa, Robert Lewandowski and Thomas Muller meant Pep Guardiola's side had the three points wrapped up inside the first 20 minutes at the Allianz Arena.
The hosts were forced to play the majority of the second half with only 10 men, as Badstuber was sent off after bringing down Olympiacos forward Brown Ideye when he was through on goal.
Yet despite the numerical disadvantage, Bayern added a fourth goal through Kingsley Coman, taking their tally in this season's competition to 17 goals in five matches.
Despite the heavy defeat, Olympiacos still control their own destiny in the battle to reach the knockout stages.
They host Arsenal in the final round of fixtures knowing a draw will be enough to see them advance to the last 16.
Bayern simply blitzed their opponents in the opening quarter, Costa breaking the deadlock when he slotted home a rebound with his left foot, with visiting goalkeeper Roberto having initially parried Jerome Boateng's long-range effort.
Lewandowski doubled the home side's lead, albeit in rather fortuitous circumstances.
Coman's weak shot unwittingly struck the Polish forward, who then reacted quickly to fire the loose ball into the bottom left corner.
A third goal arrived when Arjen Robben's clever header back into the centre of the area allowed an unmarked Muller to tap home.
The only disappointment for Bayern in an opening half they dominated was the loss of Robben to injury. The Dutchman headed straight down the tunnel after being replaced by Joshua Kimmich but Bayern later tweeted his withdrawal was merely precautionary.
Badstuber didn't last the full 90 minutes either, though his departure was due to him being shown a straight red card.
After allowing Ideye to get on the wrong side, the defender compounded his initial error by hauling the former West Brom player to the ground.
Arthur Masuaku curled the resulting free-kick over the bar, and that was about as close as Olympiacos came to scoring while playing 11 against 10.
Bayern, however, had no problems adding to their tally. Coman bravely headed home before colliding with Roberto, leaving the Frenchman with a bloody nose as a reward for his gallantry.