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.
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
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.
