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A thunderous Sergio Aguero volley had put the home side ahead before Drogba rose highest to head in an equaliser from a Florent Malouda cross.
Drogba then sidefooted in at the second attempt, after his first shot had been saved, to put Chelsea in front.
But Aguero curled in a late 25-yard free-kick to deny the Blues victory.
Drogba was back after a three-game European ban after his wild antics following the semi-final defeat to Barcelona in last year's competition.
And his goals showed him at his powerful and clinical best but glossed over a Chelsea display which had rarely shown the kind of edge and authority which has seen them win their last four games on the bounce and score 17 goals in the process.
Source: http://news.bbc.co.uk/sport2/hi/football/europe/8337806.stm