Hosts Augsburg took a deserved lead after nine minutes when Mads Pedersen picked up the ball outside the box and fired a shot into the bottom right corner of the net.
Bayern levelled after 27 minutes when Eric Maxim Choupo-Moting collected a through ball from Serge Gnabry and beat keeper Tomas Koubek from an acute angle.
Joshua Kimmich sent Bayern ahead after 53 minutes when Sadio Mane intercepted a defensive pass from Carlos Gruezo, the ball ending up with Kimmich who scored from the edge of the box.
Choupo-Moting made it 3-1 in the 59th minute before Bayern's Dayot Upamecano breathed life into the game six minutes later when he accidentally flicked in an own goal.
Bayern struck again in the 74th minute when Alphonso Davies nutmegged Lukas Petkov in the corner before passing the ball to Jamal Musiala who buried the ball into the corner of the net.
Davies scored himself one minute into stoppage time to complete the rout.
Earlier on Wednesday, Borussia Dortmund won 2-0 at Hannover 96 thanks to an own goal from Bright Arrey-Mbi and a penalty by Jude Bellingham.
Bundesliga leaders Union Berlin comfortably beat second division FC Heidenheim 2-0 at home courtesy of goals by Tymoteusz Puchacz and Sven Michel.
