Drogba's tying goal came only two minutes after he entered the game. Ivory Coast will return to the World Cup finals along with Ghana, the only African team to have already won its group.
Cameroon and Gabon both won in Group A, so the Indomitable Lions retained their one-point lead over Gabon with one game to play.
Egypt's Pharaohs stayed alive in Group D with a 1-0 win at Zambia. They are tied with Algeria, which will regain its three-point lead if it beats last-place Rwanda in Blida on Sunday. Egypt hosts Algeria next month.
Tunisia leads Nigeria by two points in Group B. The Carthage Eagles face Kenya and Nigeria plays Mozambique on Sunday.