In front of German football bosses, 22 former Bayern greats and Bavarian political royalty, the champions left it late, scoring three goals in the second half through Thomas Muller, 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.
They have broken a string of records, including most points, most away wins and best start, en route to their first silverware of any kind since 2010.
With Bayern chasing an unprecedented treble for a German club with the Champions League and German Cup still in their sights, coach Jupp Heynckes, in his last home game for the Bavarians, still found some time to praise his team.
"This season is one for the record books," said a beaming Heynckes, who will make way for former Barcelona coach Pep Guardiola next season. "I hope the 88 points we have amassed will stand as a record for ever."
"Our season is far from over. We still want to achieve something great and when we have achieved something great then we will celebrate in a big way."
Augsburg's Alexander Manninger made two brilliant first- half saves to deny Muller and Mario Mandzukic from point-blank range and the battling visitors even hit the bar early in the second half.
But he was well beaten when Dante floated a long cross into the box and Muller 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 Muller, Lothar Matthaus and Roy Makaay.
The 68-year-old Heynckes received a standing ovation and the biggest cheer from fans before undergoing the traditional on-pitch beer shower.
"This is an amazing record in this season and it is really unbelievable. It is my sixth league title and as good as the first one," midfielder Bastian Schweinsteiger, still missing an international trophy, told reporters.
"We all know there are still some games left for us but tonight we will celebrate."
League boss and Dortmund President Reinhard Rauball handed the silver platter to Philipp Lahm, who lifted it into the Munich sky. The team then left in a car convoy to celebrate at Munich's central square.
DORTMUND STRUGGLE
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 against his former team before Naldo drilled in to complete a three-goal 12-minute spell after Sven Bender had put Dortmund ahead.
But Reus struck twice in the last s
