Douglas Costa, Robert Lewandowski, Thomas Mueller and Kingsley Coman all netted for the Bavarians, who cruised to victory despite having Holger Badstuber sent off early in the second half.
Pep Guardiola's Bayern are now certain to finish on top of Group F, while Arsenal remain in contention after Alexis Sanchez scored twice in a 3-0 win over Dinamo Zagreb in London.
They remain three points behind Olympiakos in second but they will go to Greece to decide who finishes second next month.
Barcelona earlier secured their place before kicking a ball at home to Roma thanks to a 1-1 draw between BATE Borisov and Bayer Leverkusen in Belarus.
The reigning European champions then clinched top spot in Group E in style, crushing Roma 6-1 at the Camp Nou with Luis Suarez and Lionel Messi both scoring twice.
Elsewhere, Chelsea closed in on qualification from Group G with a 4-0 win at Maccabi Tel Aviv while Dynamo Kiev kept alive their hopes by beating Porto 2-0 in Portugal.
In Russia, Zenit St Petersburg, who had already qualified, secured top spot in Group H with a fifth win in five as they beat Valencia 2-0.
Oleg Shatov gave the home side the lead after a quarter of an hour and the prolific Artem Dzyuba secured the points in the second half before Valencia defender Ruben Vezo was sent off.
Gent are second after coming from behind to win 2-1 at Lyon as Kalifa Coulibaly got a last-gasp goal.
Real Madrid and Manchester City, who play on Wednesday, had already qualified for the knockout stage after the last round of games.