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.
The hosts got off to a stronger start and also put the ball in the net before a VAR review cancelled out the goal.
They still managed to take the lead with teenager Plavlovic turning in the box and drilling home his first league goal in the 23rd minute.
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.
Bayern added a second goal deep in first half stoppage time when Davies rifled in a low shot.
Kane then tapped in his 23rd league goal in the 58th minute following a lengthy VAR review to restore Bayern’s two-goal lead before Augsburg earned an 87th minute penalty.
Neuer picked the right corner and palmed Sven Michel‘s spot kick wide but Demirovic beat him with another spot kick in stoppage time to inject some late drama into the game.
The defeat leaves Augsburg in 12th place on 21 points.