With both teams having qualified for next month's World Cup, Friday's match gave both sides a chance to limber up for the tournament with little pressure.
Bosnia, who are heading to the World Cup for the first time, dominated the match but squandered a series of opportunities to score.
Dzeko, Bosnia's all-time leading international scorer, gave the eastern Europeans the lead after just 17 minutes when he rifled a shot into the back of the net from just inside the box.
Ivory Coast's goalkeeper Sylvain Gbohouo had saved a shot from Edin Visca but his block ricocheted straight to the feet of Dzeko, who made no mistake with his shot.
Dzeko scored again in the 53rd minute, controlling Miralem Pjanic's cross with his first touch and volleying the ball into the net on his second.
Ivory Coast created some good opportunities and were finally with a goal in the last minute when Drogba, playing in his 100th international, was brought down by Anel Hadzic.
Already his country's most prolific scorer, Drogba chalked up his 64th international goal when he scored from a free kick.
Bosnia play Mexico in a friendly in Chicago on Tuesday before flying to Brazil to finish off their preparations for the World Cup, where they are drawn in Group F with Argentina, Iran and Nigeria.
Ivory Coast's next warm-up match is against El Salvador in suburban Dallas next Wednesday. The Africans are in the Group C at the World Cup, along with Colombia, Greece and Japan.
(Reporting by Julian Linden in New York)
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