They went ahead right on the stroke of half time as Gervinho curled his shot past the goalkeeper.
Salomon Kalou nearly made it 2-0 on the hour, but his fierce shot was well saved.
Drogba's header in the final two minutes nearly found the net, while Bakaye Traore and Seydou Keita both had chances to level for Mali in the dying stages. However, they were unable to convert as the Ivory Coast held on to progress. They will now face Zambia in Sunday's final.