The fourth seed, who is yet to win a Grand Slam despite his undoubted talent, angrily threw his racquet at the start of the second set as Djokovic ramped up the pressure.
Federer said that two stern encounters had set him up nicely for Nishikori on Friday. "So you see, two sets sometimes doesn't tell the truth".
The 37-year-old Federer was forced to battle through the first two matches of his title defence, first to Daniil Medvedev and then Roberto Bautista Agut. "From that standpoint, I feel like I found a rhythm". "I somehow got it done".
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He said: "I faced one [break point] and it was a set point". In all, Federer presented Coric with seven beak point possibilities. "I served, I think, 80 percent in that second set and got broken twice". It was part of the tactics, but obviously Alexander can play much better than he played tonight. Zverev will play either second-seeded Djokovic or seventh-seeded Kevin Anderson in the semifinals.
Zverev has beaten Edmund all four times they've played.
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Federer won the Australian Open at the start of this year but has had a mediocre season by his sky-high standards. Djokovic won a record fourth Shanghai Masters title with a 6-3 6-4 win over 13th-seeded Borna Coric on Sunday.
"Where I was about four months ago and where I am today is quite an extreme opposite". Many top players have skipped the Davis Cup in recent years to ease their schedule, and Zverev expects that trend to continue even with the new format, which was supposed to attract more of the star names.
Anderson had a chance to take an early lead against Djokovic but he overhit a forehand on set point in the 12th game of the match.
Coric didn't offer Federer a break point opportunity, while managing to break Federer's serve in the opening game of both sets.
Djokovic and Zverev met on clay in the final of the Rome Masters in May last year, the 21-year-old German winning 6-4, 6-3.
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I think his career is just starting and we want to do it with him, he can do it with us, giving us and giving him the best performances at the best level ".