Rafael Nadal had to withdraw due to an ab injury leaving the No. 1 ranking for now to Novak Djokovic.
After Federer had been stunned by John Millman and Nadal had fallen victim to a knee injury in a semi-final against Juan Martin del Potro, Djokovic ruthlessly overcame the Argentine 6-3 7-6 (7-4) 6-3.
Nadal, who was won 17 major titles to Djokovic's 14, added that the match had been agreed over a year ago, a long time before the recent controversy surrounding the regime emerged.
Djokovic cruised through to the quarter-finals after Dzumhur retired while trailing 6-1, 2-1.
But in the past few days, I started to feel a little bit [of an] abdominal [injury], especially when I was serving.
Turkish President Recep Tayyip Erdogan said the investigation needs to be completed swiftly and wants an extradition request for 18 suspects detained in Saudi Arabia to be put on trial in Istanbul.
Meanwhile, Roger Federer progressed to the last-16 in Paris after Milos Raonic pulled out with an elbow injury.
Federer, who won his 99th career title at the Swiss Indoors last Sunday, will next face 13th-seeded Fabio Fognini.
The win improved the Croatian's prospects of making the ATP Finals in London starting on November 11.
"It's been a hard year for me in terms of injuries, and so I'd prefer to avoid doing anything drastic", added the 32-year-old Nadal, who had a successful first half of the season, clinching his 17th Grand Slam title at the French Open in June, after triumphs in Monte Carlo, Barcelona and Rome. "Of course, I would love to [remain] No 1 but I am here to just try my best every day". "At the same time I played only nine events and got injured in two of them - both have been at Grand Slams", Nadal told ATP's official website.
John Isner was a victor and Marin Cilic and Grigor Dimitrov advanced to a Thursday tussle.
Nishikori beat Frenchman Adrian Mannarino 7-5, 6-4 while Isner battled past Mikhail Kukushkin 6-3, 6-7 (2), 7-6 (1).
There were also wins for defending champion Jack Sock Kevin Anderson, Dominic Thiem, Grigor Dimitrov, Borna Coric, Diego Schwartzman and Malek Jaziri.