Drogba, who had been carrying an injury, came on in the 62nd minute when his team was losing 1-0.
The talismanic striker's arrival immediately lifted the Ivory Coast team and Wilfried Bony and Gervinho scored with headers two minutes apart. Both goals were set up by curling crosses from defender Serge Aurier.
Coach Sabri Lamouchi's inspired substitution negated Keisuke Honda's first half goal that had given Japan the lead in a group that also includes Colombia and Greece. Colombia beat Greece 3-0 earlier on Saturday.