كتب : Mohamed Sabe
The Chelsea striker was brought down by Morocco defender Walid Regragui as he surged into the box to be awarded a penalty.
Drogba powered a low shot to beat goalkeeper Tarik El-Jarmouni who dived in the right direction.
The win put Ivory Coast in second place in Group A, trailing hosts Egypt who beat Libya 3-0 on Friday on goal difference.
Both sides gave a mediocre performance and lacked the cutting edge to score.
Ivory Coast will next take on Libya in the second round of the group stage while Morocco will face hosts Egypt on Tuesday.