Carlo Ancelotti's side had failed to defeat the Foals in the last four games but they didn't have to worry this time around as goals from Arturo Vidal and Douglas Costa in the first half secured the points for the Bavarians.
Andre Schubert's side were second best throughout the game and will have to regroup and hope they play much better in their next game than they did in this if they want to start moving up the table.
Vidal made hosts dominance count
After a cagey start to the game from both teams, Bayern started to hit their stride and finally broke through after a good spell of chances.
Vidal was the man to get the crucial first goal for the hosts as he headed home a brilliant cross from Rafinha Alcantara.
Rafinha went close to opening the scoring a few minutes before the goal himself after he made space for himself in the box but drilled his shot wide when he should have done better.
Robert Lewandowski also hit the post before the goal after a good passing move from the defending champions saw the big striker only denied by the post.
After the goal, it really was all one-sided as the visitors really struggled to get hold of the ball and create anything of note.
Costa added a second on his return from injury
Bayern finally made their dominance count just after the half-hour mark, when a cross from David Alaba found it's way to Costa at the back post and after taking one touch, he confidently curled the ball home past the helpless Yann Sommer.
Ancelotti's men continued to have all of the ball and they looked dangerous every time they went forward and if it wasn't for some last ditch tackles then Bayern would have been further in front at half-time.
Visitor's made a better fight off it in the second half
The second half was a much more even affair as the visitors saw much more of the ball than they did in the first and threatened a few times on the counter-attack to get a goal back.
Bayern also looked like a team that took their foot off the gas during the second half as they weren't going forward as quickly as they did for the majority of the first half.
They were almost punished for their slackness as a great cross into the box found Andre Hahn, who had been quiet for most of the game, but his shot on the stretch came back off the post which was so unlucky.
Apart from this effort, though, the visitors failed to create anything else and Bayern could have extended their lead late on as Alaba tested Sommer with a long-range free-kick.