Goals from Marouane Fellaini and Radja Nainggolan had put the hosts in control before the visitors produced a stirring comeback
A towering first-half header from Marouane Fellaini and a goal at the start of the second period from Radja Nainggolan had put Marc Wilmots' men in charge but the Elephants fought back impressively.
Drogba halved the visitors' deficit with 16 minutes to go before Gradel struck late on.
The draw means Belgium have not won in four contests and their form will be of concern to Wilmots just over three months out from the World Cup in Brazil.
Rated by many as tournament dark horses, the home side started impressively and it was no surprise when Fellaini, who has endured a torrid first season at Manchester United, rose highest to nod home Dries Mertens' corner after 17 minutes.
The African side posed few alarms for Belgium and the hosts ought to have made it 2-0 four minutes into the second half when Kevin Mirallas picked out Christian Benteke, only for the Aston Villa striker to shoot wastefully over the bar.
It did not look like being a costly miss when Nainggolan struck two minutes later, as the Roma midfielder fired past visiting goalkeeper Sayouba Mande.
Cote d'Ivoire appeared to be out of the contest but, not for the first time, Drogba led a dramatic recovery.
The Galatasaray man prodded in after 74 minutes after the Belgium defence had failed to clear a free-kick.
And it was more defensive uncertainty which led to the equaliser a minute into stoppage time.
Again, Belgium failed to clear their lines and Gradel steered the ball past Thibaut Courtois from the edge of the box.