The former world number one asserted that despite being unsure of getting back to the required standards of tennis, he never lost the belief in his abilities.
That trio has combined to win 10 of the past 14 championships at Flushing Meadows: Five for Federer, three for Nadal, two for Djokovic.
It is Djokovic's 13th major trophy, the fourth-highest total in the history of men's tennis. But it's also his first in more than two years.
This comes after Williams lost at the Wimbledon final to Germany's Angelique Kerber.
They participated in the two longest semifinals in the history of a grass-court tournament that dates to 1877.
They had played on and on, through 6 1/2 hours of ho-hum hold after ho-hum hold, during the second-longest match in the history of a tournament that began in 1877.
Williams will face 11th-seeded Angelique Kerber, on Saturday in a rematch of the 2016 final at Wimbledon.
Rafael Nadal won 7-5, 6-7 (7), 4-6, 6-4, 6-4 on Wednesday and earned a trip to the semifinals at the All England Club for the first time since 2011.
Isner, a 33-year-old American playing in his 41st major tournament, reached his first Grand Slam semifinal by beating Milos Raonic at the All England Club on Wednesday.
The three-time Wimbledon champion was broken in the opening game of the fourth set, but won the next four games and broke again to clinch the victory.
Federer had a match point at 5-4 in the third set, but struck a backhand into the net before the eighth-seeded Anderson broke in the following game and held serve.
Serena Williams defeated Camila Giorgi of Italy 3-6, 6-3, 6-4 to march into the Wimbeldon 2018 semis.
Federer was seen playing a cricket shot - a near perfect forward defensive push - during the match during his 4th round match.
Serena Williams faces 14th-seeded Daria Kasatkina, just two weeks after beating the Russian in a third-set tiebreaker on the grass courts of Eastbourne, tying their head-to-head record at 3-3.
Roger Federer, Serena Williams and Rafael Nadal have reached the quarter-finals of Wimbledon.
Djokovic complained to the chair umpire but the call stood — even though TV replays also showed Edmund's shot had actually landed wide.
The top-seeded Halep's exit means only one of the women's top-10 seeds remains in the tournament, Pliskova, which leaves Serena Williams as the big favourite to win her eighth Wimbledon title.
Garbine Muguruza lost 5-7, 6-2, 6-1 to 47th-ranked Alison Van Uytvanck of Belgium.
Cilic's early exit opens up Federer's path to the final even more, with No. 8 Kevin Anderson the highest-seeded player left in the Swiss star's half of the draw after No. 6 Grigor Dimitrov lost in the first round.
Suddenly "Miss Williams" has become "Mrs. Williams" in the words of chair umpires.
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