The 33-year-old, playing at his fourth Nations Cup, saw his penalty saved by Danilo and scored the opener in a seven-minute spell of the first half, then headed another midway through the second.
After Drogba took his overall Nations Cup tally to 10, Yaya Toure completed the scoring with an exquisite free-kick in the 81st minute with the stadium already half empty after disillusioned fans filed out.
"The game was as difficult as we expected, Equatorial Guinea have had a great tournament," said Ivory Coast coach Francois Zahoui, whose team have not conceded a goal. "I'm pleased we scored three goals and with the way we played."
Equatorial Guinea's Brazilian coach Gilson Paulo, who only took over the side one month ago following the resignation of Henri Michel, said he had done the best possible job in a short time.
"I knew it would be a very difficult game against experienced players with a lot of quality," he said. "I'm happy with the job we did in a short time."
Facing Ivory Coast's experienced team was clearly a bridge too far for a side consisting mainly of players from the Spanish lower league and without a single local-born player in the starting line-up.
Drogba shot low to Danilo's right but the Brazilian-born goalkeeper managed to get his fist to the ball, sending the stadium into raptures.
Drogba finished off the home team's chances when he headed in Toure's free-kick in the 70th minute, silencing the stadium.
