Amid heavy snowfall at Olympiastadion, Coman scored in the 21st minute after the returning Rune Jarstein – making his first league appearance since June – became just the second Bundesliga goalkeeper to save a penalty from Robert Lewandowski.
Dodi Lukebakio and Krzysztof Piatek had chances for Hertha in Pal Dardai's first home game since taking over as head coach for a second time but Bayern held on for the win.
Hansi Flick's side consequently opened up a 10-point lead at the summit over RB Leipzig, which faces bottom side Schalke on Sunday (AEDT).
Manuel Neuer did well to keep out Lukebakio and Jarstein matched him by denying Leroy Sane, but he tripped the former Manchester City winger to concede an early penalty.
Lewandowski was unable to score from the spot, though, as his run of 16 straight converted penalties in all competitions ended with a redeeming moment for Jarstein.
However, there was nothing the Hertha keeper could do when Coman's shot from just outside the box deflected off Niklas Stark and looped into the back of the net.
Lewandowski was denied by Jarstein before FIFA World Cup winner Sami Khedira came off the bench to make his Hertha debut.
Matheus Cunha had a chance to snatch a point for the hosts when he was released by Matteo Guendouzi in the 89th minute but his dink over Neuer drifted just wide.