In-form France winger Coman struck in the 34th minute for the German giant at the Allianz Arena, his sixth goal of the campaign for club and country.

It was given a scare in the latter stages when Marko Marin curled agonisingly wide, but Lewandowski and substitute Muller struck late on to add gloss to the result.

Tottenham's draw with Olympiacos leaves Bayern as the only side with maximum points in the group after matchday one.

Philippe Coutinho was a lively presence throughout and he threatened with a driven shot just over the bar from the edge of the penalty after the visitors failed to clear their lines.

Jander wasted a chance for Red Star when he selfishly shot from a wide angle and could only find the side-netting and soon the Serbian champions were made to pay.

With a drop of the shoulder, Ivan Perisic beat his man before whipping in an inviting left-wing cross, which Coman converted emphatically with a diving header.

Coutinho almost made it two with a trademark effort, cutting inside before wrapping his foot around a bending shot that agonisingly missed the top-right corner.

Marin was inches away from levelling when he shot just wide with Manuel Neuer rooted, and Lewandowski made Red Star pay when, with 10 minutes left, he took advantage of some tired defending to poke in from close range.

Muller added another in added time when he superbly latched onto Thiago Alcantara's free-kick cheekily flicked over the wall.