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|Serbia's Novak Djokovic returns the ball to Bosnia-Herzegovina's Damir Dzumhur during the men's singles third round tennis match of the ATP Paris Masters. (Anne-Christine POUJOULAT/AFP)|
Four-time Paris champion Djokovic made the last-eight when Bosnian opponent Damir Dzumhur retired trailing 6-1, 2-1.
Federer defeated Italy's Fabio Fognini 6-4, 6-3 as the Swiss great moved three wins away from his 100th career title.
Djokovic will replace Rafael Nadal as the world's top player on Monday after a two-year absence.
The 31-year-old's elevation is remarkable as it comes just five months after he slumped to 22 in the world - his lowest ranking for 12 years - when he was knocked out of the French Open in the quarter-finals.
Since then, however, he has won Wimbledon and the US Open, taking his Grand Slam tally to 14, winning 20 consecutive tour-level matches for the sixth time, and 29 of his past 30 encounters.
"Reflecting on what I've been through in the last year, it's quite a phenomenal achievement," said Djokovic who will face Marin Cilic for a spot in the semi-finals.
"I'm very, very happy and proud about it. Five months ago, it was highly improbable considering my ranking and the way I played and felt on the court.
"I'll probably be able to speak more profoundly about it when the season is done and hopefully if I get to finish as No. 1."
Federer, 37, who captured his 99th trophy on home ground in Basel last week, will next face Japan's Kei Nishikori who beat South Africa's Kevin Anderson 6-4, 6-4.
Third seed Federer is playing the Paris Masters for the first time since 2015 and is bidding to clinch the tournament for just the second time after winning it in 2011.
"I think both of us were far from our best, but we fought with what we had and at the end I think I maybe served a bit better in the important moments than Fabio did," said Federer who was playing his first match of the week after second round opponent Milos Raonic withdrew on Wednesday.
Nishikori, seeded 10, had lost to seventh-seeded Anderson in the Vienna final on Sunday.
However, he has a 2-6 record against Federer with his most recent win over the 20-time major champion coming in 2014.
Djokovic was guaranteed a return to the ranking summit when Nadal withdrew from Paris with an abdominal injury on Wednesday.
LONDON PLACES ON LINE
"It's not the end of the season. Rafa obviously is struggling with injuries since the US Open. But the race is still there," added Djokovic after extending his sequence of consecutive winning sets to 30, passing his previous best mark of 29 from 2015.
"Roger (Federer) is in the race. Rafa is in the race. It depends who is going to play the ATP Finals in London. So as I said, I can't be too ecstatic about it."
Cilic, the fifth seed, secured his quarter-final ticket with a 7-6 (7/5), 6-4 defeat of Grigor Dimitrov.
Cilic fired 29 winners to advance to the last eight for the third straight year.
The win also improved the Croat's prospects of making the ATP Finals in London starting on Nov 11.
"I am very close to London, to securing my spot mathematically," said Cilic, who is part of the Croatia team facing France in the Davis Cup final at the end of this month.
"In the next match against Novak it will be another big challenge. (It will be) great to play him again."
Cilic, who has beaten Djokovic just twice in 17 meetings, ended reigning ATP Finals champion Dimitrov's season.
Djokovic and Cilic were joined in the quarter-finals by Karen Khachanov who saved two match points against John Isner on his way to defeating the eighth-seeded American 6-4, 6-7 (9/11), 7-6 (10/8).
The Russian will next play Alexander Zverev after the German fourth seed beat Diego Schwartzman of Argentina 6-4, 6-2.
Austrian sixth seed Dominic Thiem reached the quarter-finals in Paris for the first time, seeing off in-form Borna Coric 6-7 (3/7), 6-2, 7-5.
Thiem, also in contention for the ATP Finals, next faces defending champion Jack Sock of the United States.
Third round results:
Jack Sock (USA) bt Malek Jaziri (TUN) 6-0, 6-4
Dominic Thiem (AUT) bt Borna Coric (CRO) 6-7 (3/7), 6-2, 7-5
Alexander Zverev (GER) bt Diego Schwartzman (ARG) 6-4, 6-2
Karen Khachanov (RUS) bt John Isner (USA) 6-4, 6-7 (9/11), 7-6 (10/8)
Kei Nishikori (JPN) bt Kevin Anderson (RSA) 6-4, 6-4
Roger Federer (SUI) bt Fabio Fognini (ITA) 6-4, 6-3
Marin Cilic (CRO) bt Grigor Dimitrov (BUL) 7-6 (7/5), 6-4
Novak Djokovic (SRB) bt Damir Dzumhur (BIH) 6-1, 2-1 - retired