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Note: This answer applies to Ataturk Airport, not the new Istanbul Airport, which is scheduled to begin serving this flight on or before 3 March 2019.
Let your flight crew on your originating flight know you have a short connection. They can open a door off the jetway for you that goes directly to the departure area and will skip the long lines.
See also the related Q&A, Need guidance on how to navigate Istanbul AtatΓΌrk Airport (IST), including Aleks G's description of this transfer door.