Gervinho and Max Gradel scored the other goals to give the Ivorians a two-goal advantage ahead of next month's return leg in the final round of preliminaries for the 2013 finals in South Africa.
Three-time winners Cameroon, however, face an uphill struggle to avoid missing out on qualification for a second successive tournament after they lost 2-0 to the Cape Verde Islands.
Nigeria, who also missed out last time, are well-placed after drawing 2-2 at Liberia while Sudan completed a thrilling 5-3 win over neighbours Ethiopia.
Emmanuel Adebayor marked his first competitive game for Togo this year with a late equaliser in a 1-1 away draw with 2012 co-hosts Gabon.
Defending champions Zambia, Ghana, Mali and the Central African Republic were also winners in Saturday's final round, first leg games, with five fixtures to be played on Sunday.
Senegal stunned the home crowd by taking a 32nd-minute lead through Dame Ndoye before Kalou equalised soon after halftime.
Papiss Cisse restored Senegal's advantage on the hour mark and the possibility of an upset against Africa's top-ranked team loomed large.
Ivory Coast, however, scored three goals in 20 minutes to turn the match around with Gervinho equalising in the 65th minute, Drogba adding a penalty soon after and Gradel scoring the fourth with five minutes to play.
Drogba also had a late effort disallowed.
Cameroon were without forward Samuel Eto'o, who is refusing to play for his country in protest against the team's management.
They face a tough task in the return leg of their tie after Portuguese-based Helton and Djanini scored in Praia for Cape Verde, who are now poised to qualify for the first time.
Victor Moses was instrumental in Nigeria's away draw in Monrovia, with the visitors' goals coming from Nosa Igiebor and an Ike Uche penalty.
Tunisia are also well set after a 2-2 draw in Sierra Leone.
Adebayor, playing just his third international in more than two years, netted a late equaliser in Libreville to give Togo hope of qualification.
Zambia, who won the last Nations Cup in Equatorial Guinea and Gabon earlier this year, made a winning start to the defence of their crown with captain Chris Katongo scoring the only goal of their qualifier at home to Uganda in Ndola.
Uganda were denied a late equaliser when Zambia goalkeeper Kennedy Mweene made an important save to deny Emmanuel Okwi seven minutes from fulltime.
The Nations Cup is usually held every two years, but is being played in 2013 to accommodate a switch from every even to every odd year.
The 16 finalists from this year's tournament play a two-legged tie against teams who won an earlier round of knockout matches to decide who goes through to the finals to be played in South Africa in January.