Thomas Mueller put Bayern on top on 34 minutes and Lewandowski netted twice in the second half to send Julian Nagelsmann's side top of Group E.
"We came to win this game and we knew that we had to show respect to Barcelona," said Lewandowski.
Lukaku headed in Cesar Azpilicueta's cross to give Thomas Tuchel's team a winning start in Group H.
"The guys who are there to score regularly for their teams are so important because one goal changes the whole momentum of the match," Tuchel said of Lukaku.
Alex Sandro headed Juve ahead and Paulo Dybala converted a penalty before Alvaro Morata notched a third for a side that has picked up just one point from three games in Serie A.
Bayern stretched their record unbeaten away run in the Champions League to 19 games by sweeping aside Barca in the first meeting between the clubs since the Germans triumphed 8-2 in a one-off quarter-final last year.
"I think it's a record, three penalties (conceded) in 36 minutes, I don't think it's ever happened to me." "We'll try and pick up three points in our next game and build momentum from there." When you have three penalties against you, a red card, I think you have to be happy with a draw," said Rakitic.
Ronaldo, the leading scorer in Champions League history, bagged his 135th goal in the competition after 13 minutes in Bern, but Swiss champions Young Boys hit back after the sending-off of Aaron Wan-Bissaka.
The Austrians missed two of three first-half penalties, with Karim Adeyemi firing wide from the spot and Luka Sucic hitting the post having earlier converted Salzburg's second penalty..Read Full Story