Roger Federer is also into the quarters in his for a 100th title.
Nishikori, who fell to Anderson in the Erste Bank Open final last week, claimed a 6-4, 6-4 win against the world No. 6 South African at the last men's event before the season-ending tour final. "(It will be) great to play him again". Djokovic's 20th consecutive win sets up a last-eight clash with Marin Cilic.
On Court One, John Isner beat Kazakh Mikhail Kukushkin 6-3 6-7 (2-7) 7-6 (7-1). The Serbian, victor of this year's Wimbledon and US Open titles, will now return to top spot for the first time in two years regardless of how far he goes in Paris.
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. "Obviously he has a big serve and big game from the back of the court, it is just a very powerful style", said Djokovic.
"We are very, very pleased with what was achieved in the last four, five months", said Djokovic.
Bulgarian ninth seed Grigor Dimitrov, who is working with United States legend Andre Agassi in Paris, went through with a 7-6 (12/10), 6-4 victory over Spain's Roberto Bautista Agut. In addition, when Novak takes the number 1 spot on Monday, that will be the seventh change at the top in 2018, the most since that insane 1999 season when we had eight big shifts in the standings.
Iran seeks European assurances as USA oil sanctions loom
India along with seven other nations have been exempted from sanctions getting imposed against them for importing oil from Iran. But senior administration officials refused to spell out the names on Friday.
The Spaniard, who has never won the indoor tournament, is making his return from the knee injury that scuppered his US Open chances.
Canada's Milos Raonic came from a set down to reach the second round with a hard-fought 6-7 (4) 7-6 (5) 7-6 (5) win over local favourite Jo-Wilfried Tsonga.
Dzumhur upset 14th-seeded Stefanos Tsitsipas 6-3, 6-3, while big-hitting Russian Karen Khachanov also advanced to the third round.
Djokovic ranked as lowly as 22nd earlier this year, before bouncing back strongly since the Wimbledon, winning 29 of his last 30 matches through to Thursday.
Lucky loser Malek Jaziri replaced Nadal and beat Verdasco 7-6 (5), 1-6, 6-3 and next faces defending champion Jack Sock.
In the quarter-finals, Khachanov will meet Germany's fourth seed Alexander Zverev, who took 80 minutes to overpower and finally subdue the scurrying defiance of Argentina's Diego Schwartzman 6-4, 6-2.