The record 20-time Grand Slam victor Federer, who won his 99th career title at the Swiss Indoors last Sunday, will next face 13th-seeded Fabio Fognini of Italy.
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.
"It was great to be here in Paris for a couple of days and practice and in terms of tennis, I think I am better than I thought one week ago", Nadal said.
For Nadal, it is the second straight year he has withdrawn from the Paris indoor tournament and he is not sure if he will play at the season-ending ATP Finals in London, starting November 11.
Nishikori, seeded 10, had lost to seventh-seeded Anderson in the Vienna final on Sunday.
Fourth seed Alexander Zverev also cruised into the last eight with a 6-4 6-2 win over Diego Schwartzman.
Djokovic, a 14-time Grand Slam champion, had slipped down to 22nd in the rankings in May as he dealt with an elbow injury.
Madison Bumgarner y Pablo Sandoval seguirán en los Gigantes
Entretanto, la opción del antesalista venezolano Sandoval era por el monto mínimo posible de $555.000 dólares. Luego volvió y tuvo un balance de 6-7 con una efectividad de 3,26 en 21 aperturas.
'In the next match against Novak it will be another big challenge.
Djokovic, looking in much sharper form than his opening match against Joao Sousa, took the set in 39 minutes and, once he had earned an inevitable break for 2-1, consoled the Bosnian, who told him at the net that he was in no shape to continue.
Austrian Dominic Thiem had to come from behind to beat Borna Coric 6-7 (3) 6-2 7-5 and his reward is a last-eight meeting with America's Jack Sock, a 6-0 6-4 victor over Malek Jaziri. Had Juan Martin was ready for London, Kei would have to beat Dominic Thiem or Marin Cilic here in Paris which is not an easy task since they both reached the quarters but the Japanese is now ready to fight at the ATP Finals, seeking a deep run after finding the right form in the closing weeks of the season.
After two players held their serves in the first two games, Federer registered his first break throughout the match and built a 4-1 lead, seeing his Italian rival throw the racquet onto the court in discontent.
Roger Federer reckoned that he felt the love of the French public sweep over him when made a long-awaited return to competitive action in Paris on Thursday to launch his bid for a 100th career title. "But I'm very happy because it means I'm moving on in the tournament".
Defending champion Jack Sock needed less than one hour to beat lucky loser Malek Jaziri 6-0, 6-4.
Djokovic was characteristically dominant on the court on Thursday, as he swept through the first set against Damir Dzumhur.