Joao Felix put the hosts in front just before the half-hour mark, which seemed enough for the Rojiblancos to secure a win. However, Thomas Muller came off the bench and restored parity from the spot in the 86th minute, after being fouled by Felipe.
Bayern Munich named a weakened side for the match, with in-form striker Robert Lewandowski not even in the matchday squad, and plausibly struggled to create many chances.
Diego Simeone's side, meanwhile, attempted 13 shots in total, more than twice as many as the reigning European champions, but failed to add a second. Now, they'll have to beat Red Bull Salzburg on the final day to secure a place in the Round of 16.
Atletico Madrid Player Ratings
Jan Oblak - 7/10
The Slovenian barely had to do anything in the match, as Bayern Munich struggled offensively without many attacking stars. Unfortunately, he couldn't keep out Muller's penalty and missed a shot at a valuable clean sheet.
Stefan Savic - 6/10
Savic once again put his body on the line to safeguard his net from Bayern Munich. Most notably, he made a vital clearance towards the end to divert Hernandez's searching cross towards the box.
Jose Gimenez - 6/10
He wasn't really tested by Bayern Munich's attacker,s but the Uruguayan was always on hand to clear any danger.
Mario Hermoso - 7/10
What a colossal shift in defense from the Spaniard. He denied Bayern Munich with three tackles, clearances, and defensive aerial duels each.
Kieran Trippier - 6/10
He offered little in the way of attack, but was defensively sound against Bayern Munich's threat. His crosses sometimes looked wayward though.
Marcos Llorente - 8/10
One of the best performers in the match, Llorente was all over the pitch. His passing accuracy was fantastic, even assisting Felix with a pass from a tight angle. His movements in the attacking half were a constant source of threat.
Koke - 7/10
Koke was the key to ball progression and even sometimes drove forward to link up with the attackers.
Saul - 7/10
There was not much to see from him attacking-wise, but he did break Bayern Munich's play at times.
Yannick Carrasco - 7.5/10
A big threat down the left flank, Carrasco constantly drove forward to link-up with Felix and laid some good crosses too.
Angel Correa - 7/10
Even though he started up top with Felix, Correa played in a slightly more withdrawn role. He ran between the channels and fed the Portuguese with some nice through-balls.
Joao Felix - 8/10
The Portuguese sensation continued his bright start to the season with another goal. He poked home Llorente's pass from close range for this third goal in the competition, and eighth of the season overall.
Felipe - 5/10
Despite only coming off the bench, Felipe managed to be one of the worst players on the pitch. Firstly, he conceded the penalty which saw Bayern Munich and then fumbled Lodi's cross in really clumsy fashion.
Hector Herrera - N/A
The Mexican was on the field for over 10 minutes, but only touched the ball twice.
Thomas Lemar - N/A
He only came on to see out the final few minutes of the match, but almost set-up Hermoso with a nice cross.
Renan Lodi - N/A
Lodi didn't get much time to pull off anything, merely seeing out the match like a pedestrian.