First half goals from 19-year-old Aleksandar Pavlovic and Canada international Alphonso Davies plus one from the league's top scorer Harry Kane just before the hour took second-placed Bayern to 47 points.
Only a minute later, however, Bayern winger Kingsley Coman had to be helped off the pitch after what looked like a knee injury, piling more pressure on an already depleted squad.
The defeat leaves Augsburg in 12th place on 21 points.
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