Atletico were heading for the knockout rounds after Joao Felix‘s opening goal.
But substitute Thomas Muller earned an under-strength Bayern a draw with a late penalty after a foul by Felipe.
Bayern are already through to the last 16 but have now seen their 15-game European winning run ended.
However, there are more positives than negatives for the Bundesliga leaders to take from the game.
Having already won Group A and with a game against the side directly below them in the German top flight, RB Leipzig, to come this weekend, Hansi Flick opted to omit many of his star players.
Goalkeeper Manuel Neuer, midfielder Leon Goretzka and striker Robert Lewandowski did not even travel to Spain, while the likes of Serge Gnabry and Muller started on the bench, before coming on for the last 30 minutes.
But a young side that included former Chelsea academy players Bright Arrey-Mbi and Jamal Musiala equipped itself well against a much more experienced Atletico team.
Musiala, who became Bayern’s youngest ever goalscorer when he netted in September’s 8-0 win over Schalke and made his England Under-21 debut as a 17-year-old last month, was especially lively.
And while Muller’s late leveller was somewhat harsh on the home side, who had 13 attempts at goal to the visitors’ six, it was further proof of the dogged determination that complements their undoubted ability.
The result was also harsh on Felix, a player who is now starting to shine after a quiet first year following his £113m moves from Benfica.
The 21-year-old’s goal – his eighth of the season and third in five Champions League games – showcased his superb movement and predatory instinct as he darted to the near post to finish Marcos Llorente’s cross.
They will need another performance from him in eight days’ time when they visit a Salzburg side who won 3-1 at Lokomotiv Moscow on Tuesday.