Roger Federer, meanwhile, comfortably defeated Adrian Mannarino in a 6-0, 7-5, 6-4 victory to reach the quarterfinal stage.
Federer's progress through the draw has been smooth and serene, not dropping a set nor losing a service game on his way to an Open era record 53rd Grand Slam quarter-final. He then had to play on the Tuesday and was forced to quit in the second set of his quarter-final against Tomas Berdych on the Wednesday when his chronically sore serving elbow flared up. Like Federer, Nadal, and every other player in the quarters, he is also three wins away from Wimbledon glory, and is focused on writing his own story as opposed to being part of another, supposedly inevitable tale.
Del Potro trails Nadal 10-5 in head-to-head meetings - his five wins all coming on hardcourts.
Having reached the first Grand Slam quarterfinal of her career, Goerges went a step further with a comeback victory over her Dutch opponent.
"You always tend to play better against better players and I am happy to be back in the second week of Wimbledon".
It was very dark when they finished.
Djokovic, victor of three singles titles at the All England Club, will next meet Japan's 24th seed Kei Nishikori.
The surprise switch could give Anderson heart though, according to former world number one Mats Wilander, as the South African has played several matches on Court One.
World No. 130 Gulbis came through qualifying and shocked 4th seeded German Alexander Zverev in the 3rd round.
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The road to recovery following elbow surgery has been rocky for Djokovic, but there were signs of a revival during the clay-court season, which included a run to the French Open quarter-finals, while this rebirth was all-but confirmed with his display at Queen's last month.
Del Potro fell 4-1 behind in the third set after Simon broke in the third game. She is seeded 25th after missing last year's tournament while pregnant.
Despite being a three-time champion, Djokovic has featured just once on Centre Court - against British home favourite Kyle Edmund in the last 32 - in the opening four rounds.
He achieved that feat back in 2005 and 2006 when he won his third and fourth Wimbledon crowns.
"Now the matches are only going to get tougher", Djokovic said on Monday.
Giorgi, 26, had failed to get past the third round of a major since the 2013 U.S. Open. So, too, is 19-year-old Denis Shapovalov of Canada.
Garbine Muguruza, Maria Sharapova, Simona Halep, Petra Kvitova, Venus Williams, Caroline Wozniacki and Sloane Stephens have all been eliminated already.
Bertens and Pliskova had reached the fourth round at Wimbledon for the first time.
Bertens, who was contemplating retirement previous year after losing her enthusiasm for the sport, is the first Dutch woman to reach the Wimbledon quarterfinals since Michaella Krajicek in 2007. He will face Djokovic next in his first quarterfinals appearance at the All England Club.
"It was ridiculous what happened there". I didn't think that was ever going to happen. "I probably won't have another 6-0 set this week, so I'll enjoy this one".
(11) Angelique Kerber bt.
The 52nd-ranked Giorgi of Italy took the first set 6-3.