However, Bayern Munich couldn't muster a way past the obdurate defence of the visitors, who missed two good chances at the other end in the final ten minutes of the game to clinch an unlikely win.
It marked only the second time this season that Bayern Munich dropped points in the Bundesliga, a result that opens up a chance for rivals RB Leipzig to draw level with the reigning champions at the top of the table.
On that note, let's have a look at how Bayern Munich players performed in the game:
Bayern Munich Player Ratings
Manuel Neuer - 8/10
After getting tormented by Spain in Tuesday's 6-0 defeat with Germany, the sweeper-keeper was back to his best again.
In his 400th game for the club, Manuel Neuer made a superb double save in the first-half when the game was still goalless; he also smothered Leonardo Bittencourt's effort from close range to prevent a late winner for Werder Bremen.
Benjamin Pavard - 6.5/10
Benjamin Pavard was good offensively, but his positioning left plenty of space at the back for Milot Rashica and Ludwig Augustinsson to exploit. The Werder Bremen duo often drove forward on the break to give Bayern Munich some really nervy moments.
Jerome Boateng - 7/10
Jerome Boateng was slightly off the pace whenever Werder Bremen broke forward on the counter, but he was otherwise sound. The German laid the most passes in the match with 109, completing 88% of them accurately, while also winning three aerial duels and making two successful tackles.
David Alaba - 7/10
David Alaba started off as a centre-back, but Lucas Hernandez's injury prompted him to move to left-back, where the Austrian was terrific. He was a constant danger down the flank with his movements upfield and delicious crosses.
Lucas Hernandez - N/A
The latest star to join Bayern Munich's growing injury list, Lucas Hernandez, was taken off after only 20 minutes into the match following a collision with Gebre Selassie.
With Alphonso Davies out for a significant period of time, Hansi Flick will be hoping that the Frenchman's injury isn't too serious.
Javi Martinez - 6.5/10
Javi Martinez was outpaced by Josh Sargent in the build-up to the opening goal of the game, but the Spaniard improved thereafter and made two key clearances.
Kingsley Coman - 7/10
One of the best players for Bayern Munich against Werder Bremen, Kingsley Coman was at the heart of everything good that came from the home side. He constantly kept Werder Bremen on their toes with buccaneering runs down the flanks before heading the champions level just after the hour mark.
Thomas Muller - 6.5/10
The Raumsdeuter (interpreter of space)'s spatial expertise couldn't help Bayern Munich against Werder Bremen, as the visitors left almost no space for him to exploit. Besides his aerial prowess, Thomas Muller won three duels offensively and made three successful tackles, but there was nothing spectacular about his performance on the night against Werder Bremen.
Jamal Musiala - 7/10
In his first Bayern Munich start, highly-rated England U21 international Jamal Musiala impressed in bits and parts. His first touch was class, and he also linked up well with Robert Lewandowski at times.
Douglas Costa - 7/10
Douglas Costa's pace and work-rate continued to be awesome; however, that didn't translate into anything substantial for Bayern Munich against Werder Bremen.
Robert Lewandowski - 6/10
It was an uncharacteristically poor game for Robert Lewandowski, who did not just failed to score but could not muster a single shot on target too.
The Poland international was effectively boxed up by Werder Bremen's defence, and even the introduction of Serge Gnabry and Leroy Sane in the second half couldn't liberate Robert Lewandowski.
Ratings of Bayern Munich Substitutes
Leon Goretzka - 8/10
An impact substitute, Leon Goretzka was colossal in the Bayern Munich midfield. He did not just assist Coman with a lovely cross from over the top, but he also denied Bittencourt a potential late winner with a superb last-ditch block.
Leroy Sane - 7/10
Leroy Sane was energetic, pacy and eager during his cameo. In fact, he even created a wonderful chance for Chuopo-Moting towards the end which the latter incredibly wasted from point-blank range.
Serge Gnabry - 6.5/10
Serge Gnabry had a stinker against Werder Bremen. He looked exhausted and even skied an effort after a neat one-two with Choupo-Moting.
Eric Maxim Choupo-Moting - 6/10
Eric Maxim Choupo-Moting was largely anonymous in the game, but when a gilt-edged chance presented itself, the Cameroonian international blazed his effort into the stands when the easiest thing in the world was to tap the ball home.