Two goals from former Arsenal player Serge Gnabry and a goal from Robert Lewandowski put the German champions into total control of their last 16 tie against Chelsea.
This leaves Chelsea with a 3 goal deficit to turn around when they visit the Allianz Arena next month.
A first half of Bayern dominance, but no breakthrough
The first half was one of few chances, though through the system that he had chosen to go with, you could see that Chelsea manager Frank Lampard was expecting Bayern to have much of the ball.
This was proven to be true as Chelsea were limited to just a handful of chances on the break, with Olivier Giroud having the best chance for the blues after almost getting on the end of Mason Mount's fine delivery.
Willy Caballero pulled off a string of saves to keep the scores level but it wasn't until just after the half-hour mark that we saw a flash of what was to come, Thomas Muller's brilliant headed effort cannoning off the post.
Gnabry's quick fire double gives the German side control
Bayern came racing out the blocks after half-time and it wasn't long before they were ahead.
Gnabry converted Lewandowski's brilliantly timed pass into the net to give them the lead just past the 50 minute mark.
It was Gnabry again three minutes later that picked the ball up on the left-hand side of the penalty area, after another well weighted pass from Lewandowski, and brilliantly finished into the bottom right corner of the goal.
That was Gnabry's sixth Champions League goal of the season after scoring four against Tottenham Hotspur earlier in the season and it gave the Bundesliga leaders total control of the match, and indeed the tie.
Lewandowski takes match beyond Chelsea
Having been provider for Gnabry's two goals, Polish striker Robert Lewandowski turned finisher late on to further Chelsea's woes.
19-year-old left back Alphonso Davies showed a great bit of pace to reach the by-line before pulling it back for a Lewandowski tap-in.
That all but finished Chelsea's hopes of a revival and ensured that they will have it all to do when they travel to Munich on March 19.
Alonso sent off late on
To make matters worse for Chelsea, they will be without both Marcos Alonso and Jorginho for the second leg of the tie.
Alonso was sent off after a VAR review by referee Clement Turpin for catching Lewandowski across the face whilst running for the ball.
Meanwhile, Jorginho received a yellow card in the second half and he will now also miss the second leg due to accumulating too many bookings in the Champions League this season.