Drogba, back after a three-match suspension, scored twice in the final ten minutes to put Chelsea in front only for second half substitute Sergio "Kun" Aguero to score his second with a 90th minute equaliser.
Chelsea knew a win would see them through to the next phase but in the end a draw was enough due to FC Porto's 1-0 win at APOEL in Tuesday's other group match.
Drogba, who had not played in the Champions League since May after he was hit with a three-match ban for berating the referee after the semi-final defeat to Barcelona, showed his striking prowess.
"It was a good game but frustrating because we didn't win it," said Drogba.
"I have played many Champions League games with Chelsea in the past and to be honest I am just happy to be back on the pitch.
"We have qualified which is great although it would have been nice to do it with a win."
Aguero had put Atletico into a 66th minute lead but the Ivory Coast forward headed an equaliser on 82 minutes and struck again on 88 minutes.
Argentine Aguero equalised in the final minute for Atletico's first goal in the competition and ended Chelsea's 100% record but they still progress.
Chelsea now hope to be back in Madrid in May for the final at the Santiago Bernabeu as they aim to win the Champions League for the first time in their history.
With qualification wrapped up Carlo Ancelotti's side can concentrate on the crunch title clash with Manchester United at Stamford Bridge on Sunday.
Atletico, third from bottom in Spain, have just two points in the group and can now only hope for a spot in the Europa League as they prepare for a weekend derby against Real Madrid.
"We have a good team here and we will do everything to try and stay in Europe," said Aguero. "It would not be a failure to go into the Europa League."
Chelsea routed Atletico 4-0 in their first match in London a fortnight ago without Drogba and they have the worst defensive record in the Spanish top-flight so they must have feared the worst.
Ancelotti resisted the temptation to rest stars with Manchester United on the horizon and even welcomed back Ashley Cole who recovered from a knee injury to begin at left back.
His opposite number "Quique" Sanchez Flores played a somewhat conservative 4-5-1 with Diego Forlan as the main striker.
Atletico were far from defensive despite their formation and were shooting from long range to try and steal a goal.
Jose Antonio Reyes almost scored in the 20th minute with a super curling shot but Petr Cech tipped the effort over the crossbar.
Chelsea had plundered an impressive 17 goals in their last four matches but didn't threaten too much. However, they went close on the half hour mark when Salomon Kalou, a two-goal hero against Atletico in the first game, headed just wide.
Six minutes into the second half Drogba watched on in agony as his free-kick was touched onto the post by goalkeeper Sergio Asenjo.
Flores decided to throw on Aguero for Florent Sinama Pongolle and it reaped rewards when the Argentine volleyed in from 15 yards out 12 minutes after coming on.
It was Atletico's first goal in this season's Champions League and the first Chelsea had conceded in Europe.
Drogba should have equalised in the 73rd minute after being put through on goal but dragged his shot poorly wide.
However he found his touch in the 82nd minute heading in Malouda's cross and he outmuscled his marker to score again in the 88th minute before Aguero completed a crazy final ten minutes.
Chelsea knew a win would see them through to the next phase but in the end a draw was enough due to FC Porto's 1-0 win at APOEL in Tuesday's other group match.
Drogba, who had not played in the Champions League since May after he was hit with a three-match ban for berating the referee after the semi-final defeat to Barcelona, showed his striking prowess.
"It was a good game but frustrating because we didn't win it," said Drogba.
"I have played many Champions League games with Chelsea in the past and to be honest I am just happy to be back on the pitch.
"We have qualified which is great although it would have been nice to do it with a win."
Aguero had put Atletico into a 66th minute lead but the Ivory Coast forward headed an equaliser on 82 minutes and struck again on 88 minutes.
Argentine Aguero equalised in the final minute for Atletico's first goal in the competition and ended Chelsea's 100% record but they still progress.
Chelsea now hope to be back in Madrid in May for the final at the Santiago Bernabeu as they aim to win the Champions League for the first time in their history.
With qualification wrapped up Carlo Ancelotti's side can concentrate on the crunch title clash with Manchester United at Stamford Bridge on Sunday.
Atletico, third from bottom in Spain, have just two points in the group and can now only hope for a spot in the Europa League as they prepare for a weekend derby against Real Madrid.
"We have a good team here and we will do everything to try and stay in Europe," said Aguero. "It would not be a failure to go into the Europa League."
Chelsea routed Atletico 4-0 in their first match in London a fortnight ago without Drogba and they have the worst defensive record in the Spanish top-flight so they must have feared the worst.
Ancelotti resisted the temptation to rest stars with Manchester United on the horizon and even welcomed back Ashley Cole who recovered from a knee injury to begin at left back.
His opposite number "Quique" Sanchez Flores played a somewhat conservative 4-5-1 with Diego Forlan as the main striker.
Atletico were far from defensive despite their formation and were shooting from long range to try and steal a goal.
Jose Antonio Reyes almost scored in the 20th minute with a super curling shot but Petr Cech tipped the effort over the crossbar.
Chelsea had plundered an impressive 17 goals in their last four matches but didn't threaten too much. However, they went close on the half hour mark when Salomon Kalou, a two-goal hero against Atletico in the first game, headed just wide.
Six minutes into the second half Drogba watched on in agony as his free-kick was touched onto the post by goalkeeper Sergio Asenjo.
Flores decided to throw on Aguero for Florent Sinama Pongolle and it reaped rewards when the Argentine volleyed in from 15 yards out 12 minutes after coming on.
It was Atletico's first goal in this season's Champions League and the first Chelsea had conceded in Europe.
Drogba should have equalised in the 73rd minute after being put through on goal but dragged his shot poorly wide.
However he found his touch in the 82nd minute heading in Malouda's cross and he outmuscled his marker to score again in the 88th minute before Aguero completed a crazy final ten minutes.