It was the 4th successive win for Djokovic over Federer, and the Serb will play against Russia's Karen Khachanov.
14-time grand slam champion, Djokovic, won the first set 7-6.
The incident took place during the first set that Djokovic was leading 4-3 with an advantage while returning Federer's serve. There I won the tournament and here I played in the semis and it needed somebody of Novak's calibre to beat me. He was given a huge ovation by the crowd after his win. "He protects his serve very well", Federer said. "I have an enormous amount of support around the world".
Federer, the 2011 champion in Paris, last beat Djokovic at the ATP Tour Finals in 2015 and was comprehensively beaten by his long-time rival in the Cincinnati Masters final on the eve of the US Open this year.
"I'm having the best season, so far", Khachanov said. Federer's down the T serve was returned well by Djokovic straight in the middle and the Swiss ace took his time before whipping it to Djokovic's right to what looked like a sure victor.
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Cilic, who defeated 31-year-old Djokovic in the final at Queen's Club in the summer, was a break ahead again for a 2-1 lead in the decider.
An ace gave Cilic set point and he took it when Djokovic sent a backhand wide.
Brimming with confidence in a season which has seen him go from No. 22 in the rankings in May to No. 1 when they are released on Monday, and in which he also added the U.S. Open to his Grand Slam haul, Djokovic created pressure throughout.
Djokovic broke his racket in frustration and then broke Cilic straight back, after which the momentum shifted back in his favor as Cilic lost to him for the 16th time in 18 meetings.
"That's why he is who he is", Djokovic said, admiringly. "I was kind of going up and down". "I'm confident and I'm in the final, so I'm really happy about it".
"It's intense, it's good tennis, we care about winning, we don't like losing".
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The Russian did not let his level slip at all as he clinched victory and a major scalp on a big stage.
"I'm in the semifinals of a Masters 1000 only for the fourth time", Thiem said.
The sixth-seeded Thiem next faces unseeded Karen Khachanov of Russian Federation in their first career meeting.
Khachanov won the Kremlin Cup in Moscow last month for his third career title.
Zverev had treatment on his right shoulder late in the first set and made a string of unforced errors.
"When you lose a close match like this you always have regrets", Federer, who remains one title shy of 100 career trophies, told the crowd, according to the Washington Post. "I told him to tell him to keep it down a little bit because he was going a little bit too much over the edge". "And I'm looking forward to a rest now and a good preparation for London (ATP Finals)".
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