Man of the match Lennart Karl made headlines by becoming the youngest player to start a Champions League match for the club at 17 years and 242 days.
He was also the second-youngest German to start in the competition.
He then became Bayern's youngest scorer in the Champions League and the youngest German to score in the tournament when he opened the scoring after just five minutes.
Harry Kane added a quick-fire second with 14 minutes on the clock and Luis Diaz got on the scoresheet with 34 minutes.
Nicolas Jackson then sealed the result with his 79th minute strike.
The result saw Bayern move onto nine points from three games, level with leaders Paris Saint-Germain.
Brugge have picked up three points from their opening three matches.
Speaking after the game, Bayern boss Vincent Kompany told his club's website: "It was a good performance. We maybe could’ve scored more goals, but we kept a clean sheet and overall delivered a very good home performance.
"In addition, some of the young players showed that they can help us in this season – that was important."
Kompany added that it is important for the club to keep their new young star grounded.
"He was great tonight and will get a lot of hype but I'm not a fan of hype. I'm a fan of performance, education, and calm."
Looking ahead to their upcoming encounters, the Bayern boss concluded: "In terms of the next games, obviously we've got great opponents in PSG and Arsenal but we want to win every game.
"The path to the next round isn't easy, we know that. Now it's about continuing to pick up points – in the league, in the cup and in the Champions League. The winners of the Champions League won't be decided yet. What counts for us is progressing – that's our job."
Karl was, meanwhile, delighted with his performance, adding: "I'm very happy about my goal and about my performance.
"It's just a huge amount of fun with the team. We give our all in every training session, which is carrying over into the matches.
“Everything's just working very well right now. I can learn a lot from the guys. To also be 'Player of the Match' today makes me very happy, of course, but I have to keep working and build on this.”
Brugge head coach Nicky Hayen admits his side were second best against the German giants. He said on Bavarian Football: "The key for Bayern was their play in behind. We were running after them 80 percent of the time.
"You can't win that way. We weren't at our best, had too much fear in some situations, although we did play better in the second half.
“This was a lesson for us today. Bayern are an example worldwide.”
Bayern Munich have made it clear that Michael Olise is not for sale, with sporting director Max Eberl confirming there is no release clause in the French winger's contract despite growing interest from top European clubs.
Seventeen-year-old Lennart Karl produced a memorable performance as Bayern Munich eased to a 4–0 win over Club Brugge in the Champions League.
Real Madrid defeated Juventus 1-0 in their UEFA Champions League clash at the Santiago Bernabeu on Wednesday evening to make it three wins out of three.
Barcelona returned to winning ways in emphatic fashion, thrashing Olympiacos 6-1 in the Champions League.
