Nadal said it was "an exceptional circumstance" that he has remained on top of the tennis world after turning 30, alongside Federer, 36, and Djokovic, 31.
Williams has complained before at being drug-tested more than other American tennis players this year.
Ramkumar, who ended a runner-up at the Newport event last week, lost 4-6, 4-6 to American world number five Taylor Fritz.
The Rogers Cup is a tuneup for the US Open. Williams last played it in 2014, when she reached the semifinals. She won the event three times when it was played in Toronto.
Germany's Angelique Kerber kept world No.4, after having claimed the spot a week earlier thanks to her first-ever Wimbledon title victory.
The 23-year-old from Chennai beat the American 6-4 7-5 to become the first Indian in seven years to make it to the singles title round on ATP World Tour.
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.
The world number 161 has made his first ever entry into the last four of any ATP tour.
Leander Paes bowed out after losing his doubles quarter-final at the Hall of Fame Open grasscourt tournament in Newport.
Leander Paes made a winning return to competitive tennis with American partner Jamie Cerretani at the ATP Hall of Fame Open in Newport.
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.
Angelique Kerber won her first Wimbledon championship by stopping Serena Williams' bid for a record-equaling 24th Grand Slam title.
Djokovic sent the strongest signal yet he is back at the top of tennis by reaching his fifth Wimbledon final with a 6-4, 3-6, 7-6 (9), 3-6, 10-8 victory over rival Rafael Nadal.
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.
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