The trouble in Dakar overshadowed qualification for Ghana, Mali, Morocco, Nigeria, Tunisia and holders Zambia who are all through to the finals in South Africa in January.
Drogba's latest talismanic performance proved too much for the Senegal fans who invaded the pitch, threw objects and lit small fires in the packed stands after their team went 2-0 down and 6-2 behind on aggregate in the final round tie.
Striker Drogba's free-kick just after half-time extended the Ivorians' two-goal lead from the first leg and then converted a 71st minute penalty which sparked the violence.
The riot, which highlighted the explosive nature of the African game, put a dampener on a day of excitement on the pitch across the continent with Zambia needing a penalty shootout win to ensure they can defend their crown at next year's finals.
Tunisia also scraped into the finals on away goals after being held 0-0 by modest Sierra Leone at home in Monastir, following a 2-2 draw in last month's first leg.
Morocco's Youssef Al Arabi scored five minutes from time, after earlier missing two gilt-edged chances, to give Morocco the decisive third goal in a 4-0 win over Mozambique in Marrakesh where they overcame a 2-0 first-leg deficit.
Ghana were first to qualify by beating Malawi 1-0 away in Lilongwe for a 3-0 aggregate triumph thanks to Afriyie Acquah's debut goal. Mali went on the rampage with a 4-1 win over Botswana on the road in Lobatse to advance 7-1 on aggregate.
