Galatasaray striker Didier Drogba opened the scoring in the fifth minute by neatly converting a penalty after a trip on Gervinho, and the hosts were two up on 12 minutes when Bordeaux defender Ludovic Sane inadvertently directed the ball past his own goalkeeper from Gervinho's cross.
Roma forward Gervinho was again the provider when Salomon Kalou made it 3-0 within four minutes of the restart, the Lille striker bursting through the middle and coolly slotting a low shot home for his 22nd international goal.
That looked to have put the Ivorians firmly in the driving seat to qualify for a third straight World Cup finals, but Papiss Cisse volleyed home deep into stoppage time to give Senegal hope heading into next month's second leg in Casablanca.
In Saturday's other play-off first leg, Burkina Faso edged Algeria 3-2 in Ouagadougou thanks to a controversial late penalty from Aristide Bance.
The Algerians twice battled back from a goal down, second-half strikes from Sofiane Feghouli and Carl Medjani cancelling out Jonathan Pitroipa's effort in first-half stoppage time and a Djakaridja Kone goal.
However, the referee pointed to the spot four minutes from time on the advice of his assistant for a dubious handball offence against Essaid Belkalem, and Fortuna Dusseldorf frontman Bance - who earlier had a first-half spot-kick saved - kept his composure when given a second chance to convert from 12 yards.