Champions League -03/11/2009
Atletico hold Chelsea
Sergio Aguero also netted twice, coming off the bench to break the deadlock on 66 minutes with a stunning volleyed strike.
It seemed to be enough to give Atletico a first Champions League win of the campaign, but Drogba popped up with a header on 82 minutes and a rebound strike two minutes from time to break the hearts of the home fans.
Yet Atletico refused to give up hope, and Aguero's superb dipping free kick in injury time gave the hosts the point they richly deserved - even if Porto's win at APOEL means that it is Chelsea and the Portguese side who will qualify from Group D.
Atletico came into the match without having scored a goal in the Champions League so far this season, but had the better of the opening half as Simao and Jose Antonio Reyes consistently looked like opening up the visitors.
Chelsea looked dangerous only through occasional chances, with Salomon Kalou's 32nd minute header their best chance of the opening period.
As the second half got under way Drogba nearly opened the scoring with a brilliant sidefooted free kick that Sergio Asenjo tipped on to the post.
With both sides consistently frustrated, it took a moment of genius from Aguero who latched on to John Terry's poor clearing header to thump a stunning volley cleanly past Petr Cech.
Atletico appeared to be heading for victory as they continued to dominate, but Florent Malouda's perfect cross to Drogba with eight minutes left brought the scores level.
When a long ball through from Ashley Cole put Drogba through six minutes later his first shot was well-saved, but the rebound fell kindly and he lashed the ball in the net unopposed to seemingly give the Blues a victory they scarcely deserved on the run of play.
Yet Aguero won a free kick a minute into injury time and justice was done as his brilliant effort curled and dipped over the wall into the right edge of the net beyond the hands of Cech.
Drogba might still have had a chance to win it for Chelsea after he appeared to dive and win a free kick 60 seconds later.
But as the free-kick was laid back to the Ivorian striker, it gave the Atletico wall crucial seconds to charge out and deny Drogba his hat-trick and Chelsea the win.