Bayern Munich have won four league games out of four this season
Thomas Muller scored a 90th-minute penalty as champions Bayern Munich came from a goal down to continue their 100% start in the Bundesliga.
Pepe Guardiola's side trailed to Alexander Esswein's spectacular goal for Augsburg just before half-time.
But Bayern, who begin their Champions League campaign away to Olympiakos on Wednesday, drew level through Robert Lewandowski with 13 minutes left.
Muller made it four league wins out of four after Douglas Costa was fouled.
Winger Kingsley Coman, signed from Juventus at the end of August, made his debut for the champions as a second-half substitute as Guardiola's side eventually wore down their opponents.
Bayern, beaten 1-0 at home by Augsburg late last season after they had already clinched the title, looked in danger of defeat again after Esswein's opener.
The midfielder's volley flew past keeper Manuel Neuer two minutes before half-time.
Bayern had several chances to draw level as they applied pressure after the break, with Augsburg goalkeeper Manuel Hitz saving well to keep out Xabi Alonso's free-kick.
Lewandowski stabbed in the equaliser after Hitz had reacted brilliantly to push out a shot from Muller, who then kept his composure to strike the winner from the spot following Markus Fulner's foul on Costa.