Porto's 1-0 win at APOEL Nicosia meant the Portuguese team and Group D leaders Chelsea both went through. Atletico, third with two points from four games, can still claim a spot in the Europa League.
There were few chances in the first hour at the Calderon although Chelsea goalkeeper Petr Cech had to dive full length to palm away a curling shot from former Arsenal winger Jose Antonio Reyes in the 20th minute.
Drogba, back in European action after a three-match suspension, also went close when Atletico keeper Sergio Asenjo deflected his effort on to the post just after the break.
Atletico had not scored in this season's Champions League, including a 4-0 drubbing at Chelsea last month, but went ahead after 66 minutes thanks to a spectacular strike from substitute Sergio Aguero.
John Terry's headed clearance looped up to the Argentina forward and he smashed a volley past Cech from 15 metres.
MILESTONE APPEARANCE
Drogba, on his 50th Champions League appearance for the Londoners, equalised by heading in a Florent Malouda cross in the 82nd minute.
The Ivory Coast striker then raced through the defence to give Chelsea the lead six minutes later, firing in at the second attempt after Asenjo blocked his first effort.
Aguero, who had replaced the ineffective Florent Sinama Pongolle after 54 minutes, capped a fine performance with a curling free kick to level for Atletico in the final minute.
Chelsea coach Carlo Ancelotti said: "He (Drogba) is in very good form at the moment, just look at how he works. He scored two goals, did very important work and we hope he can play many more games.
"It was a difficult match, Atletico played very well but we had very good direction after our first goal."
Atletico coach Quique Sanchez Flores, who replaced Abel Resino at the struggling La Liga club on October 23, said the draw would lift his team for Saturday's match at home to city rivals Real Madrid.
"The players have been under a lot of pressure this week and this was an important result that sets us up for the next game," he said.
