The German champions, who had defender Holger Badstuber, back from injury, sent off early in the second half with a straight red card, were unstoppable in the opening 20 minutes, scoring three times to put the game to bed early.
"We wanted to play our game from the start, with a lot of motivation and drive. We wanted to get an early goal and not have to reach the 70th minute with the game tight," scorer Thomas Mueller said.
Douglas Costa struck after eight minutes, Robert Lewandowski doubled the lead in the 16th with Mueller adding another four minutes later as dazed Olympiakos found no answer to the continuous attacks.
Kingsley Coman headed in their fourth goal in the 70th as Bayern moved up to 12 points ahead of their final game at Dinamo Zagreb on Dec. 9. Olympiakos, in second place on nine, need a point against Arsenal to secure a spot in the last 16.
Badstuber, making his first start following his muscle injury in April, was too slow for Brown Ideye in the 53rd minute, holding on to the quick Nigerian forward outside the box to get his marching orders on a miserable comeback for the injury-plagued Germany international.
"This should be a lesson for us," warned Bayern coach Pep Guardiola of the unnecessary foul by Badstuber. "If that happens in a knockout stage game then you are eliminated."
Bayern, in spectacular form having lost just once in all competitions, had put Olympiakos under early pressure and it paid off with Brazilian Costa drilling in on the rebound.
Poland striker Lewandowski doubled their lead with his fifth goal in five group games, picking up a Coman effort to fire while an easy tap-in by Mueller from an Arjen Robben header that caught the defence completely off guard made it 3-0 for the hosts.
Olympiakos, who had won their previous three group games, had to wait until the 44th for their first chance, with Luka Milivojevic sending a free kick wide.
"It is a heavy defeat but if you want to challenge such an amazing team you have to be the top of your game," said Olympiakos coach Marco Silva. "We weren't tonight. We did not fight as much as we should have. So we now have to get a result in our final game (against Arsenal)."
The Greeks enjoyed a bit more possession but Coman got in on the act heading in Mueller's nod for Bayern's 14th goal in their three group home games.
(Reporting by Karolos Grohmann, editing by Ian Chadband)
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