In front of German football chiefs, 22 former Bayern greats and Bavarian political royalty, the champions left it late, scoring three goals in the second half through Thomas Mueller, Xherdan Shaqiri and Luiz Gustavo.
It was a 28th win in 33 league games - with one league match left - for sensational Bayern, who weeks ago secured their 23rd German league title and 22nd since the introduction of the Bundesliga half a century ago.
Augsburg's Alexander Manninger made two brilliant first- half saves to deny Mueller and Mario Mandzukic from point-blank range and the battling visitors even hit the bar early in the second half.
But Austrian Manninger was well beaten when Brazil international Dante floated a long cross into the box and Mueller rose high at the far post to head in.
Franck Ribery took on four Augsburg players and threaded the ball to Shaqiri, who turned and scored in the 81st before Brazilian Gustavo completed the win with a low drive three minutes from time.
In a glitzy post-game ceremony, Bayern players were called out of the dugout one by one, their walk to the podium flanked by former greats such as Franz Beckenbauer, Gerd Mueller, Lothar Matthaeus and Roy Makaay.
Coach Jupp Heynckes received a standing ovation and the biggest cheer from fans in his last home game for the club, before undergoing the traditional on-pitch beer shower. Heynckes will make way for former Barcelona coach Pep Guardiola at the end of the season.
League boss and Dortmund President Reinhard Rauball handed the silver platter to Philipp Lahm, who lifted it into the Munich sky as the team chases an unprecedented German treble of titles with the Champions League and German Cup in their sights.
Dortmund were less convincing, needing two late goals from Marco Reus to escape with a 3-3 draw at VfL Wolfsburg.
Former Dortmund striker Ivan Perisic struck twice in the first half against his former team before Naldo drilled in from close range to complete a three-goal 12-minute spell after Sven Bender had put Dortmund ahead.
But Reus struck twice in the last six minutes to snatch a draw for second-placed Dortmund.
Schalke 04 wasted their chance to secure fourth place with a game spare after losing 2-1 to visitors VfB Stuttgart and now face Freiburg next week, who edged past relegated Greuther Fuerth 2-1, who become the first Bundesliga team not to win a home game in a season.
Freiburg are fifth on 51, a point behind Schalke, and the winner next week will play in the Champions League qualifying rounds.
Sweden's Branimir Hrgota scored a hat-trick to steer Borussia Moenchenglabdach to a 4-2 victory over Mainz 05 and maintain their hopes of clinching a Europa League spot next season.
At the other end of the table, Hoffenheim's chances of staying up all but vanished with a 4-1 demolition by visiting Hamburg SV.
Hoffenheim are in 17th place on 28 points - two behind Augsburg, who are in the relegation playoff spot in 16th - and need to win at Dortmund next week.