The victory puts the German side on nine points after four games, three behind leaders Paris Saint Germain and six ahead of third-placed Celtic, and their superior record against the Scots guarantees them a top-two spot in the group.
Though the hosts started well, Coman broke the deadlock for Bayern in controversial fashion in the 22nd minute, appearing to handle a long ball from goalkeeper Sven Ulreich before firing home following a horrendous mix-up in the Celtic defence.
After creating the goal, Ulreich had to come to his side's rescue early in the second half, getting down smartly to steer Stuart Armstrong's shot behind for a corner.
Callum McGregor put Celtic back on level terms in the 74th minute, latching on to James Forrest's clever pass before sliding the ball between Ulreich's legs.
The lead lasted only three minutes as Martinez headed Bayern back in front, sustaining a nasty cut above his eye in a clash of heads with Celtic defender Nir Bitton in the process.
Celtic shifted to a three-man backline as they chased another equaliser but even with six minutes of time added due to the injuries to Martinez and Bitton, the Hoops could not fashion an equaliser.
In the other game in Group B PSG hammered bottom side Anderlecht 5-0 to make it four wins in four games for the French champions.
(Reporting by Philip O'Connor; Editing by Clare Fallon)
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