"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 the month.
"Roger (Federer) is in the race".
The win also improved his chances of qualifying for the ATP Finals, the season-ender for the top eight men's players, in London starting on Nov 11.
It helped him to maintain the remarkable spell of form that has seen him rise from number 22 in June to the top of the game again.
Federer, who has not competed in Paris at either the French Open or indoor Masters since 2015, received a standing ovation after making a winning comeback in Bercy following his late decision to compete after his 99th triumph in Basel on Sunday.
Although Djokovic leads Cilic 15-3 overall, Cilic won two of their past three matches - including two years ago in the Paris Masters quarterfinals.
Japanese Nishikori beat Frenchman Adrian Mannarino 7-5 6-4 while American Isner battled past Mikhail Kukushkin 6-3 6-7 (2-7) 7-6 (7-1).
The U.S. Open champion won four of the last five tournaments he has entered, including Wimbledon, the U.S. Open and most recently the Shanghai Masters.
Brazil's market rise after presidential election
He will oversee the transition from Rio this week and fly to the capital Brasilia next week, Lorenzoni added. His chief economic advisor is Paulo Guedes, a University of Chicago-trained free-market economist.
Djokovic, who knew on Wednesday he would be world No.1 next week after Rafael Nadal's withdrawal from the tournament through injury, was leading 6-1 2-1 when Bosnian Dzhumur retired at 6-1 2-1 after succumbing to a back problem. "The doctor says if I continue the abdominal maybe can break and can be a major thing".
A double break of serve put Federer 4-1 up before Fognini broke back with a backhand victor down the line.
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. It's just a very powerful style of tennis. "If he has a high first serve percentage, then it's obviously a big challenge to play him because he's got a really big game from back of the court".
Zverev next faces unseeded Karen Khachanov.
World number two Djokovic broke his opponent's serve four times to extend his winning run to 19 matches.
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.