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The Serb outlasted Federer in just over three hours to prevail 7-6 (8/6), 5-7, 7-6 (7/3).
Zverev is the first German to reach the final of the season-ender since Boris Becker lost to Pete Sampras in 1996.
Comments made by French player Julien Benneteau suggesting Federer is given preferential treatment by tournament organisers also threatened to disturb him.
Djokovic overcame nagging flu to defeat Marin Cilic 6-4, 6-4 .
Federer kept his time on court to a minimum with a masterclass of serve-and-volley tennis.
Second seed and five-time champion Federer, 37, made it 18 wins in 18 second round appearances in New York by seeing off error-plagued Frenchman Benoit Paire 7-5, 6-4, 6-4.
The 20-time Grand Slam champion had been struggling with injury at the Australian Open, where he made a semifinal exit to eventual champion Novak Djokovic, and has not played since.
Tennis pundits have often suggested that Djokovic gets infuriated as well as galvanised by overwhelming support for Federer and Nadal when he locks horns with them, but the 32-year-old from Belgrade offered a different view.
The 38-year-old has been cutting down on the number of tournaments he plays over the last few years in a bid to prolong his career.
The current world No. 1 has 17 Grand Slam titles to his name - two behind Rafael Nadal and three fewer than Roger Federer - and said he has no doubt in his ability to overtake the other members of the so-called 'Big Three.'
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