Maximilian Eggestein put Werder Bremen in front in the opening half before Kingsley Coman equalised after the break. However, the winning goal proved elusive for the reigning champions, as the River Islanders put on a defensive masterclass.
Josh Sargent wasted two big chances in the final ten minutes of the game that could have helped the visitors snatch a late win, but they'll be content to have picked up a point at one of the most intimidating grounds in Europe.
On that note, here are the five major talking points from the match:
#1 Bayern Munich's injury woes deepen after latest casualty
Barely 20 minutes into the match, Bayern Munich full-back Lucas Hernandez trudged off the pitch with a knock to his leg after clattering with Gebre Selassie, which compounded his side's burgeoning injury woes.
The reigning champions were already without Joshua Kimmich, Alphonso Davies and Corentin Tolisso for the Werder Bremen game, but the Frenchman's injury further slims manager Hansi Flick's options.
While David Alaba will now slot into the left-back position, as he did against Bremen, Bayern Munich are seriously running thin in defence. So, Kovac has no option but to look towards the academy players to reinforce his squad.
Players like Tanguy Nianzou and Marc Roca, who featured in the Bayern Munich squad against Bremen, may have to step up to the first team.
#2 Werder Bremen end their 22-game losing streak against Bayern Munich
Werder Bremen came into the match on the back of 22 consecutive defeats to Bayern Munich, the longest such streak in a fixture since the inception of the Bundesliga in 1963.
That's quite some record. So, you'd be forgiven for not giving the minnows any chance in the match, but they ripped the script against Bayern Munich and put on a spirited performance to hold the champions to a very creditable draw.
The River Islanders, wary of Bayern Munich's attacking prowess, sat deep to block all the passing lanes and even cut off all the supply lines to Robert Lewandowski, who looked far from his best on the night.
David Alaba and Kingsley Coman did some good work down the flanks, but last-ditch tackles from the Werder Bremen defenders ensured that any potential danger was nipped in the bud itself.
In fact, out of 16 attempts on goal, the Bundesliga champions mustered only two on target. Bremen themselves missed two good chances at the other end in the final ten minutes of the game to win the match outright, but their stoic defending ensured that they garnered a point against Bayern Munich for the first time since 2008.