The former PSG youngster volleyed a deserved winner for the German champions, who dominated until the latter stages when Kylian Mbappe came off the bench.
In the first half, Sergio Ramos’ last-ditch tackle denied Jamal Musiala, Eric Maxim Choupo-Moting went close with a header and Coman shot wide of the near post.
Just before the break, PSG keeper Gianluigi Donnarumma got down well to hold Joshua Kimmich’s low drive.
The goal arrived in the 53rd minute when Paris-born Coman drifted unmarked into the box from wide on the right and hit a cushioned volley underneath Donnarumma.
Donnarumma went some way to making amends with a stunning point-blank save to tip Choupo-Moting’s effort onto the crossbar.
Mbappe, a substitute after recovering from injury, twice had the ball in the net late on as PSG rallied, but both goals were ruled out for offside.
Bayern’s Benjamin Pavard will miss the second leg after he was sent off for a second booking for bringing down Lionel Messi in stoppage time