The result left Bayern top of Group B on 15 points, seven more than Tottenham Hotspur who joined them in the last 16 after fighting back from two goals down to beat Olympiakos Piraeus 4-2 at home.
Bayern pinned Red Star back from the start and came close three times through Lewandowski and Kingsley Coman before Leon Goretzka fired them into a 14th-minute lead with a superb header.
The Germany midfielder rose above his markers to steer a perfect Philippe Coutinho cross from the left past goalkeeper Milan Borjan, who was left clutching nothing but air.
Lewandowski had a goal disallowed shortly before halftime after a quick VAR review ruled that Corentin Tolisso handled the ball when he teed up the Poland striker.
A vociferous band of around 2,000 visiting Bayern supporters lit some two dozen flares early in the second half, seemingly igniting Lewandowski’s onslaught against a hapless Red Star who were nonetheless roared on by their own faithful.
The Pole converted a 53rd-minute penalty after Milos Degenek handled in the box and made it 3-0 on the hour from a fine assist by Tolisso.
He headed in the fourth soon afterwards from a Benjamin Pavard cross and stunned Red Star again in the 68th minute. Tolisso completed the rout in the dying minutes with a simple finish.
Jose Mourinho’s first home game as Tottenham Hotspur manager suffered a false-start but ended in victory as his side recovered a two-goal deficit to beat Olympiakos Piraeus 4-2 and reach the last 16.
Olympiakos, bottom of Group B, stunned the hosts with goals by Youssef El Arabi and Ruben Sabedo inside the opening 20 minutes but Tottenham responded to sweep the Greeks aside.
Dele Alli’s goal on the stroke of halftime proved crucial and two goals from Harry Kane and one from Serge Aurier after the break made sure Spurs will finish runners-up in the group.
Six days after Mourinho was hired following the sacking of Mauricio Pochettino, the Portuguese two-time Champions League winner has already won two games and while the fans were not exactly singing his name, they went home happy.
Paulo Dybala curled in a free kick from the unlikeliest of angles to give Juventus a 1-0 win over Atletico Madrid, which left the Spaniards with a battle to secure a round-of-16 place.
Juventus, already qualified, won the free kick just outside the penalty area and near the goal-line but the narrow angle did not deter the Argentine who fired his shot over the wall and in off the crossbar in the 45th minute.
The Turin side, with 13 points from five games, made sure of winning Group D with one match to spare.
Atletico Madrid, beaten 3-0 on the same ground last season when they were on the wrong end of a Cristiano Ronaldo hat-trick, were left on seven points after their second successive defeat in the group, one ahead of Bayer Leverkusen.
Paris St Germain scored two late goals in the space of three minutes to battle back for a 2-2 draw at Real Madrid and secure top spot in Group A at the Santiago Bernabeu.
Real had sealed their place in the knockout stages for a record-extending 23rd successive year thanks to Club Bruges’ 1-1 draw at Galatasaray earlier while PSG had also already qualified.
Yet they still served up a thrilling game with top spot on the line.
Karim Benzema knocked into an empty net to give Real the lead in the 17th minute and doubled the advantage with a 79th minute header.
Yet Kylian Mbappe immediately reduced the deficit down the other end in the 81st minute before Pablo Sarabia equalised in the 82nd.
PSG’s fightback added to concern in the stands after Real winger Eden Hazard hobbled off in the second half with an ankle injury, although substitute Gareth Bale almost snatched a winner when he struck the post in added time from a free kick.