And even though Federer provided some early resistance in Coric's match-winning service, the 20-time grand-slam champion could not find a breakthrough to survive.
The first set went with serve, and some big serves at that, until Djokovic grabbed the break to go 4-2 up.
Federer will play eighth-seeded Kei Nishikori, a finalist in Tokyo last week, in the quarterfinals.
"It was one of the best matches of my life", Coric said.
Second seed Djokovic prevailed over Anderson at the All England Club and took his winning run to 16 matches by beating the South African 7-6 (7/1) 6-3 in one hour and 44 minutes. "But I will play tennis next year, yes", he said.
Second seed Djokovic, who has returned to his brutal best this season with Grand Slam wins at Wimbledon and the U.S Open, will surpass Federer as world number two when the next edition of the ATP rankings are released on Monday.
The 21-year-old world No. 5 Zverev, who was seeded fourth, conceded the first break with a wide forehand in the sixth game as Djokovic rallied to a 5-2 lead before breaking the German again to take the first set.
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Coric finished off Federer in style with the final two points an ace and a sizzling forehand crosscourt victor.
"I mean, my standard level nowadays is better than in the past year, that's for sure".
Bautista Agut stunned the Swiss world No. 2 in the second set after he broke three times to force a decider.
"He has improved a lot and he has established himself as a top player".
The 6-4, 6-4 victory over the 11th-seeded Briton seals Zverev's place in the season-ending ATP Finals in London next month, which bring together the top eight men.
It's going to require that plus more to stay there.' The Basel native also spoke about what he did after the US Open. "It's going to be definitely a close match", said Djokovoic.