Recalled after missing Group H victories over Rwanda and Burundi, Drogba levelled on the stroke of half-time and snatched the 74th-minute winner in Ghana capital Accra.
Benin had stunned the 'Elephants' by taking an early lead through Seidath Tchomogo as they chased a victory that would have lifted them into first position on the table.
The fixture was moved from Abidjan for security reasons as Ivory Coast has seen increasingly violent unrest following a disputed presidential election result with incumbent Laurent Gbagbo refusing to accept defeat.
Striker Salomon Kalou had the ball in the net only for Chelsea team-mate Drogba to be ruled offside before Tchomogo punished sloppy defending to edge the 'Squirrels' ahead.
Former African Footballer of the Year Drogba equalised on the stroke of half-time and snatched the match-winner after being set up by Kader Keita before a 30,000 national stadium crowd.
Ivory Coast have nine points, Benin four, Rwanda three and Burundi one at the halfway stage of the mini-league and it will be all over by early June if the Ivorians win in Cotonou and the Rwandans fail to win in Bujumbura.
Peter Utaka and Ikechukwu Uche bagged two goals each as Nigeria eventually built on a great start to thump Ethiopia 4-0 in Abuja and close the gap on Group B leaders Guinea to a single point.
This was the first competitive match in charge for new 'Super Eagles' coach Samson Siasia and he could not have wished for a better start as Denmark-based Utaka had the ball in the net with less than a minute on the clock.
But it was eight minutes after half-time before Utaka was on target again and a couple of late strikes from Uche meant Ethiopia conceded four goals for the second time in three qualifiers.
Sudan remained hot on the heels of Group I leaders Ghana thanks to a 3-0 triumph over Swaziland in Omdurman with Mohammed Bisha scoring in each half before Mohammed al-Tahir netted in the final minute.
Ghana and Sudan have accumulated seven points each with the former topping the table because they have scored one goal more and it looks like a two-team race to the finishing line with Congo and Swaziland far behind.
Short link: