The result mean Bayern are German league champions for the 28th time in their history, and it was the sixth year in a row they have won the Bundesliga since their treble-winning season in 2013.
Augsburg took a shock lead through an own goal by Niklas Suele, but the Bavarians roared back as Corentin Tolisso, James – who then assisted Arjen Robben – and Sandro Wagner all scored.
The result leaves Bayern 20 points clear with five league games left and underlined their absolute dominance of the Bundesliga.
With one eye on Wednesday's Champions League quarter-final second leg against Sevilla, in which Munich hold a slender 2-1 lead, coach Jupp Heynckes gambled by resting his stars.
Top scorer Robert Lewandowski, plus Thomas Mueller, Thiago Alcantara, Mats Hummels and Javi Martinez all started on the bench.
Sevilla would have encouraged by the comedy of errors in Bayern's defence that led to Augsburg's goal.
Jerome Boateng lingered over a back pass and Colombian forward Sergio Cordova robbed him of possession, sending Boateng tumbling to the turf, clutching his hamstring.
Cordova's shot was blocked by Bayern goalkeeper Sven Ulreich, but the ball ricocheted into Suele's face and into Bayern's goal to stun the visitors on 18 minutes.
However, Munich were 2-1 up by the time half-time came when Joshua Kimmich's cross picked out Tolisso unmarked in the area to header Bayern level on 32 minutes.
Bayern then laid on a top-class goal to take the lead at Augsburg's WWK Arena.
Kimmich was again involved, firing a pass across goal after combining with Robben for Juan Bernat, who backheeled the ball which James fired home seven minutes before the break.
The Colombian then ensured the title was heading to Munich for their third.
He hooked the ball back into play at the far post for Robben to drill his shot inside the near post on 62 minutes.
Ribery celebrated his 35th birthday with a cameo appearance for the final eight minutes before Wagner headed home Bayern's late fourth.
The Bavarian giants will formally lift the Bundesliga shield after the final day on May 12.
Elsewhere, second-from-bottom Cologne suffered a blow to their survival hopes as they were held to a 1-1 draw by Mainz.
An early goal by Cologne's Germany defender Jonas Hector was cancelled out as Pablo De Blasis headed an equaliser for Mainz five minutes into the second half.
With five games left, Cologne are six points behind Mainz, who are 16th, which carries a relegation play-off berth against the third-best team in the second tier at the end of the season.
Wolfsburg, who are just above the bottom three, won 2-0 at Freiburg in a match featuring two sides just above the bottom three and fighting to stay up.
With just two minutes gone at the Schwarzwald Stadion, Wolves striker Daniel Didavi held off his marker and fired past despairing Freiburg goalkeeper Alexander Schwolow. He added a second with seven minutes remaining.
Thorgan Hazard came off the bench to score twice as Borussia Moenchengladbach climbed to eighth with a 2-1 win at home to Hertha Berlin.
Salomon Kalou gave Hertha an early lead, but Hazard come off the bench to score on 75 minutes, then net a late penalty.