"That's it", Federer said.
"I wish I could tell you all these answers, but I really don't know".
But in the ninth game of the deciding set, Federer made the breakthrough on his opponent's serve, pumping his fist as another hard-won victory loomed into view.
"I wouldn't be so dedicated to this sport if I didn't believe that I can achieve great heights", Djokovic said.
Federer, a two-time champion in Shanghai, will next face 13th-seeded Borna Coric.
Zverev will play Kyle Edmund after the Briton defeated Nicolas Jarry of Chile 7-6 (5), 6-3. Federer was his usual aggressive best, smashing returns at Nishikori's feet and touching the lines with second-serve returns in their eighth FedEx ATP Head2Head meeting (Federer leads 6-2).
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"I mean, my standard level nowadays is better than in the previous year, that's for sure".
The top four players in the world - Nadal, Federer, Djokovic and Juan Martin del Potro - had already qualified for London.
That run includes titles at the US Open and Cincinnati Masters.
Zverev next takes on the in-form Djokovic, who was forced to dig deep in the first set before seeing off Kevin Anderson in a repeat of their Wimbledon final. Djokovic's serve has not been broken this week in 37 service games.
"I just feel like the date of the Davis Cup is really bad, especially for the top players", said Djokovic, echoing the strong sentiments of Zverev a day earlier.
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The 31-year-old says he is back close to the kind of blistering form that has brought him 14 Grand Slams.
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.
The world number three was too good for the tall South African, winning 7-6 (1) 6-3 in an hour and 42 minutes on the hard courts of the Chinese city.
The first set went with serve, and some big serves at that, until Djokovic grabbed the break to go 4-2 up.
The victory gave the 21-year-old Zverev a tour-leading 49th match win of the year. Dominic Thiem, who lost his opening match this week, sits in second place with 48 match wins this season. "Obviously I don't want to stop here". "I think it's going to be tough".
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