Coman prodded the ball in at the far post in the last minute of normal time to cancel out Junior Adamu's first-half opener and save Bayern from a first away defeat in the competition since 2017.
Bayern arrived in Austria looking to bounce back from their shock defeat to Bundesliga minnows Bochum on Saturday, but there were early signs of the same defensive wobbles which had plagued them at the weekend.
A mistake from Niklas Suele opened up a chance for Brenden Aaronson after just a few minutes, as Salzburg snapped at the heels of the Bayern back line.
A soaring long ball from Mohamed Camara opened Bayern up on the counter-attack, and Adamu curled the ball in with an elegant first-time finish.