The Spanish giants were the better side on the day as they thrashed the Bundesliga team by 4 goals to 1.
Raphinha, who was the captain of the side for 60 minutes, led the charge with a hat-trick and an impressive overall performance.
The Brazilian opened his account in the first minute before he extended the lead by two goals after Lewandowski restored Barcelona's lead.
Harry Kane pulled parity for Bayern Munich, minutes after his first was disallowed by the Video Assistant Referee (VAR) as being offside with his toe.
However, after the break, it was all Barcelona, and Raphinha netted a deserved hat-trick in the 56th minute.
Hansi Flick's men enjoyed their day out, running circles around their opponents, and still maintained control even after extending their lead.
On the other dugout, Vincent Kompany failed to capitalise on the home team's high defensive line. They fell into the offside trap three times.
First H2H win for Barcelona in 7 matches.
Meanwhile, tonight's result is the first win for Barcelona in seven meetings against Bayern in the competition.
Bayern Munich had previously won the last six encounters, scoring 22 goals in the process.
The six-time champions still have a superior head-to-head record over the five-time winners. Bayern Munich have won 10 out of 14 of these clashes in the UEFA Champions League.
Tonight's 4-1 victory makes it Barcelona's third in this battle against the Germans.
Barcelona have won two of their first three league phase games while Bayern have only managed one win out of three.