Bayern survives Augsburg scare to close gap in Bundesliga
Gnabry almost replied moments later before Coman volleyed in Joshua Kimmich's cross from close range in the 17th minute.
However, Augsburg went back in front in the 23rd when Ji Dong-won sent an unstoppable volley from around 15 meters (16 yards) in under the crossbar.
Robert Lewandowski hit the bar as Bayern again sought a response and it came in first-half injury time as Coman sent a shot through goalkeeper Gregor Kobel's legs.
Bayern then took the lead in the 53rd and again Coman was involved, this time setting up Gnabry's shot inside the far post.
Manuel Neuer was back in the Bayern goal after two weeks out with a hand injury, a timely return given Tuesday's Champions League game at Liverpool, as coach Niko Kovac was able to field his strongest side.