Lewandowski strikes again as Bayern see off Red Star
After Kingsley Coman gave Bayern a first-half lead, Lewandowski poked home ten minutes from time for his ninth goal in six matches before Thomas Mueller added a stunning late third.
The hosts were stuttering to a slender win before Lewandowski capitalised on two mistakes in the Red Star defence for a classic poacher's goal.
"We had the whole game under control, we just scored too few goals," Lewandowski told Sky.
"I'm very happy that I scored and that we played well as a team."
The margin of victory will please Bayern head coach Niko Kovac after his side peppered the Serbian team's defence and enjoyed a huge share of possession.
However, Red Star came within a whisker of equalising just before Lewandowski struck when their captain Marko Marin fired narrowly wide with Bayern goalkeeper Manuel Neuer beaten.
The German champions are not having things their own way so far in the Bundesliga and Saturday's 1-1 draw at early leaders RB Leipzig left Bayern fourth in the table, two points adrift.
However, they remain a force to be reckoned with and last lost a Champions League home game in December 2013.
It took just over half an hour for them to take the lead, capitalising on 70 percent possession.
With the away defence hanging back, understandably worrying about Lewandowski, Coman slipped his marker and headed home from fellow winger Ivan Perisic's pin-point cross from the left flank on 34 minutes.
It could have been 2-0 going into the break as Philippe Coutinho, on loan from Barcelona, audaciously flicked the ball into the net with his heel, but was narrowly offside.
Lewandowski squandered an open goal, firing over with an extravagant volley rather than a simple tap-in, with an hour gone just after Perisic had hit the crossbar.
Marin caused nervous looks in the Bayern defence when he fired wide of the diving Neuer, and the post, before Lewandowski struck.
Substitute Mueller showed his class, having replaced Coutinho, when he fired home a floated Thiago Alcantara free-kick for the best goal of the night in injury-time.