Chelsea soaked up almost constant Bayern possession but in Drogba they still had some menace in attack, the Ivorian failing to connect with one presentable chance after 73 minutes as the tension reached unbearable levels in the stadium.
Chelsea's dogged resistance was finally broken in 83rd minute when Muller arrived at the back post to bounce a header into the net from Toni Kroos's deep cross.
Muller was buried under his joyous team mates as Bayern appeared to have clinched the trophy but there was to be a sting in the tail.
With two minutes remaining, Chelsea earned their first corner and when the ball was swung in Drogba climbed high to crash a header past Neuer.
Image: Chelsea's Didier Drogba, right, celebrates after scoring the decisive shootout penalty during the Champions League final soccer match between Bayern Munich and Chelsea in Munich, Germany Saturday May 19, 2012.