Didier Ya Konan and Lacina Traore were the other scorers as the Elephants extended their unbeaten run to 22 matches, including the 0-0 draw with Zambia in this year's African Nations Cup final which the Ivorians lost on penalties.
Austria had slightly the better of the first half with Marko Arnautovic and David Alaba coming close with long-range shots and Marc Janko missing a golden chance from close range.
The game changed completely when Ya Konan powered through the Austria rearguard and fired into the roof of the net one minute before halftime.
Chinese-based Drogba came off the bench in the 59th minute and scored almost immediately with a 25-metre effort which squirmed under the body of Austria goalkeeper Heinz Lindner.
Traore added the third when he burst past his marker and fired past Linder from the edge of the area.
Ivory Coast's last defeat in 90 minutes was against Poland in November 2010.
They are warming up for the African Nations Cup in January which will almost certainly be the last chance for several of the current crop of players, including former Chelsea striker Drogba, to win the title.
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