Last season's finalists produced a hard-fought performance at the Vicente Calderon to pocket a monumental victory over the German giants to go top of Group D in Europe's premier club competition.
Yannick Ferreira-Carrasco's first-half goal proved the difference at the end of 90 minutes as Diego Simeone's Los Rojiblancos continued their journey towards Champions League redemption.
Bayern had a golden chance to level five minutes into the second half but Thomas Muller headed into the side netting when perhaps he could have done better.
In the 67th minute, Carrasco saw an opening to give Atleti a two-goal lead but was denied by Neuer before Robert Lewandowski's header 10 minutes was inches wide for Bayern.
On 82 minutes, Atletico were awarded a penalty when Filipe Luis was brought down in the area by Arturo Vidal but Griezmann could only fire his 12-yard effort into the crossbar in what was a huge letoff for Carlo Ancelotti's men.
In the end, luckily, the missed penalty did not effect the final result as Atletico held on for a deserved there points with Bayern unable to pierce their strong defensive wall.
2016/17 UEFA Champions League - Group D