Drogba equalised with a powerful header with two minutes of normal time left after Thomas Muller had headed Bayern 1-0 in front after 82 minutes.
Drogba then turned villain when he tripped Franck Ribery in the box early in extra time to concede a soft penalty but Arjen Robben’s weak penalty was well saved by Petr Cech.
The score remained locked at 1-1 by the end of extra time, which meant that, for the second time, Chelsea’s fate in a Champions League final would be decided by penalties.
In the shoot-out Philip Lahm, Mario Gomez and goalkeeper Manuel Neuer scored for Bayern while David Luiz, Frank Lampard and Ashley Cole netted for Chelsea.
Ivica Olic and Juan Mata traded missed penalties before Bastian Schweinsteiger hit the post, paving the way for Drogba to score the 10th penalty. He duly did so, sending Chelsea’s 17,500 fans at the Allianz Arena into raptures.
It will be remembered as especially memorable for the way in which Chelsea overcame the disadvantage of playing away in the German side’s stadium while have four key players banned.
There had been a carnival atmosphere in Munich throughout the day as tens of thousands of replica-shirted supporters descended on to the main square and central bars and pavement cafes to down steins in the sunshine.
It was replicated in the thunderous noise at the Allianz Arena,
A huge human wall of red and white, representing the Bayern masses, was in place a full hour before kick-off, almost unique in this day and age. The Chelsea fans filtered in more slowly, with reports they had been delayed travelling by metro to the stadium on the outskirts of the city.
Before kick-off, Roberto Di Matteo had taken a gamble by submitting a team-sheet that included the name of Ryan Bertrand for the first time in a Champions League fixture.
The 22-year-old former trainee pushed up from his normal left-back position to provide balance and defensive know-how on the left side of midfield, a role that he filled capably for 70 minutes.
David Luiz and Gary Cahill returned to central defence after lengthy injury lay-offs (five and three-and-a-half weeks respectively) with hamstring injuries, John Obi Mikel and Frank Lampard protected the defence while Bertrand, Juan Mata and Salomon Kalou were the three attacking midfielders behind Didier Drogba.
Without four suspended players – who all watched helplessly in their suits from the touchline - it was a make-do-and-mend formation. Solidity had got Chelsea through this far and Di Matteo was not going to change the script and go all gung-ho in what could prove to be his last match as manager.
Bayern, without three suspended players of their own, plumped for an attacking formation, with Toni Kross dropping back to partner Bastian Schweinsteiger and Mario Gomez filling in between the brilliant wing duo Arjen Robben and Franck Ribery.
Feeding off the passion and noise of their fans, Bayern were quickest out of the blocks and dominated the opening half. Schweinsteiger controlled the midfield to provide a platform for a red siege on the blue goal.
The error-prone Jose Bosingwa provided the first heart-in-the-mouth moment when he miscued a Lampard pass in the six-yard box. Shortly afterwards, the lively Robben tore through on goal and shot low and hard from a tight angle only for Cech to improvise smartly at his hear post.
Chelsea had to wait until the 34th minute to register their first shot of the game but Thomas Muller’s wasteful volley immediately afterward seemed to stir them into action and Salomon Kalou tested Manuel Neuer with a stinging shot from a tight angle.
Chances continued to go begging for Bayern. Gomez was the biggest culprit, firstly failing to tame a mis-cued Ribery cross that reached him just outside the six-yard box and then shooting wildly over the bar.
By half-time, Bayern had registered 13 shots to Chelsea’s two, an accurate reflection of their dominance. The only stat that mattered, though, was the 0-0 scoreline.
Immediately after the break, Robery tore down the left flank and sent in a left-footed missile that was athletically cleared by David Luiz.
Flares were lit in the top tier of the Bayern end, creating visibility problems. Chelsea continued to fight fires lit by the effervescent home side on the pitch, with Ashley Cole making a brilliant defensive clearance.
It was backs-to-the-wall stuff, just like the 180 minutes against Barcelona. Roman Abramovich, watching in the VIP area, looked inscrutable but might have wondered how all his largesse had been reduced to simple British qualities of yeoman defending and plucky resourcefulness.
Ribery had the ball in the back of the net only for it to be ruled out for off-side and Bayern were unfortunate when a strong hand ball shout, after Cole handled a Philip Lahm cross, was rejected.
By the 70-minute mark, Chelsea had blocked 11 shots in the match, more than any other team in any other Champions League game this season.
Di Matteo’s team had their best opportunity soon afterwards, when Neuer dropped the ball and it fell to Drogba’s feet. Clearly surprised, he scuffed the shot and the Germany No1 gratefully grasped it.
Bayern continued to carve out opportunities and finally made their dominance count when Muller headed in at the far post after 82 minutes.
The Germany international stole in at the back post to direct Schweinsteiger’s centre into the ground, and for Chelsea fans, agonisingly over the head of Cech and into the net off the underside of the bar.
It was due reward for Bayern’s complete dominance of territory and chances and sent the Allianz Arena, Bayern’s home ground, into a frenzy.
But six minutes later the hitherto subdued Drogba made Bayern pay for their profligacy when he met Frank Lampard’s corner with a powerful header from the edge of the six-yard box after stealing in front of his marker
This carried the match into an extra time marked by Cech’s excellent save, before the agonising arrival of penalties.