BATE next month will see them finish second.
A draw between Bayern and Olympiakos in Germany would have taken both teams through but Pep Guardiola’s team showed no mercy for their visitors as they raced into a three-goal lead inside the first 20 minutes.
Douglas Costa got the opener and Robert Lewandowski scored his 28th goal in 25 games this season before Thomas Mueller tapped in the third.
Holger Badstuber was sent off early in the second half on his return after his latest lengthy lay-off but Kingsley Coman added a fourth.
“It’s always important to finish the group first,” Bayern captain Philipp Lahm told Sky.
“That brings an advantage in the knockout stages that you play the second leg at home. It’s a good way to finish the year.”
While Bayern secured top spot in Group F, Arsenal kept their hopes alive by beating Dinamo Zagreb 3-0 at the Emirates Stadium.
Mesut Ozil headed the Premier League side ahead and Alexis Sanchez added a brace, meaning the Gunners can still qualify for the last 16, provided they win at Olympiakos next month by at least a two-goal margin or by winning by a one-goal margin having scored three or more goals.
The situation appears rather more straightforward for Chelsea, who cruised to a 4-0 win over Maccabi Tel Aviv with Gary Cahill, Willian, Oscar and Kurt Zouma on target.
The other game in Group G saw Dynamo Kiev win 2-0 at Porto with Andriy Yarmolenko netting a first-half penalty before Derlis Gonzalez wrapped up the points.
Just two points separate Chelsea, Porto and Dynamo Kiev but Jose Mourinho’s side need only draw at home to the Portuguese club next month to go through.
“Very important, especially with what happened in Porto we really needed to win this match, and also important to get two victories in a few days,” Mourinho told BT Sport.
“I hope morale comes, tranquility comes, confidence comes.”
Zenit St Petersburg, who had already qualified for the last 16, made it five wins out of five in Group H by beating Valencia 2-0 in Russia.
Oleg Shatov and Artem Dzyuba scored in each half before Valencia defender Ruben Vezo was sent off.
Gent leapfrogged Valencia into second with a 2-1 victory away to Lyon that eliminated the French team from all European competition.
Jordan Ferri had put Lyon ahead but Danijel Milicevic levelled with a free-kick before Kalifa Coulibaly’s last-gasp winner.