Chukwubuike Adamu beautifully curled in the opener for Salzburg, who looked like they could hold out for more than 70 minutes to seal a first-leg victory.
But Bayern made their dominance of the ball count when Coman levelled in the 90th minute to make honours even ahead of the second-leg at the Allianz Arena.
Julian Nagelsmann will be hoping his side can get the job done in the return leg.
The German champions had an off day as Salzburg defended brilliantly to keep them at bay for the majority of the match.
Bayern are already six points clear in the Bundesliga and it looks likely they will break a long-standing record in Europe's top five leagues by winning their tenth league title in a row come May.
Only Juventus in Italy's Serie A have also achieved this.
Salzburg, meanwhile, will be frustrated at allowing five-time Champions League winners to level so late on.
They are also building an unassailable lead at the top of the table in Austria, 14 points ahead of second-placed Wolfsberg.
More to follow…