Bayern stormed into a 3-0 lead after just 27 minutes and although Chelsea cut the deficit to just one thanks to goals from Marcos Alonso and Michy Batshuayi, they could not force an equaliser against their opponents, who are managed by their former boss Carlo Ancelotti.
Chelsea started brightly in the second game of their tour of Asia but they fell behind after just six minutes when Rafinha - who has netted just four goals in 201 appearances for Bayern - drilled a 30-yard strike into the net via the post.
It gave the Bundesliga side the platform they required to seize control of the contest and six minutes later, they doubled their advantage through Thomas Muller, who volleyed home at the back post after meeting James Rodriguez's cross.
James - who has recently joined on a two-year loan from Real Madrid - should have made it three before the 20-minute mark but he somehow fired over after being provided with an opportunity inside the box.
Chelsea were on the back foot and it got worse for Antonio Conte's side on 27 minutes when Muller curled a delightful shot into the bottom corner from 25 yards.
A break in play allowed Conte to let his players know what he thought of them, and it had the desired effect as they dominated the closing stages of the first half.
Alonso, Batshuayi and Gary Cahill all had chances before added-on time, but the Premier League side eventually got a goal back when Alonso met Victor Moses's cross and lashed an effort past Tom Starke and into the far corner.
It took a while for anything significant to happen during a lacklustre start to the second half, but Bayern eventually regained their rhythm and looked like scoring at every given opportunity.
Firstly, Marco Friedl set up Rodriguez who sent a header past the post, before Chelsea stopper Thibaut Courtois pulled off an excellent block when the Colombian was provided with an opening much closer to goal.
With 20 minutes remaining, Chelsea began to offer a response but they were not showing the same clinical touch as against Arsenal on Saturday, with both Batshuayi and Willian failing to make the most of chances and David Luiz striking the post with a deflected effort.
However, with five minutes left, they finally moved to within one goal of levelling the match as Batshuayi scored from close range after debutant Alvaro Morata had flicked the ball into his path from a Cesc Fabregas corner.
Chelsea tried to push for an equaliser but Bayern were able to hold firm as they overcame the disappointment of slipping up against both Arsenal and AC Milan by registering an impressive win over the English champions.