Del Potro needed five match points to prevail in a match suspended on Monday night under fading light and stretched four hours and 24 minutes in duration.
Victory helped Del Potro advance to the last eight at the All England Club for the first time since 2013 and it is the first time since in 2012 that he has qualified for the last eight at consecutive Grand Slams. But the 26-year-old underdog isn't ruling out an epic upset against Williams. The seventh-seeded player was defeated by Kiki Bertens 6-3 7-6.
Finally free off a painful and persistent elbow injury and blissfully content again in his private life, the Serbian plays another comeback star in Kei Nishikori for a drought-breaking semi-final berth.
The top-ranked Nadal bludgeoned 37 winners to take down unseeded Czech Jiri Vesely 6-3, 6-3, 6-4 and reach the last eight for the first time in seven years.
Federer took his tally of consecutive sets won on London's hallowed lawns to 32 with a 6-0 7-5 6-4 dispatch of unsafe French left-hander Adrian Mannarino.
For Kevin Anderson it was a day of firsts on Monday.
However, the Frenchman did manage to earn a break point - the first Federer had faced in the tournament - as his opponent served for the set and then dug deep to stay with the Swiss in the second.
On the women's side of the draw, Serena Williams is back in the Wimbledon quarterfinals for the 13th time after beating Russian qualifier Evgeniya Rodina 6-4, 6-2.
During his first set, Federer's unique style of shot catching Wimbledon's attention leading it to be dubbed as an nearly "cricket" style with their Twitter account asking the ICC to rate Federer's shot.
It will be 32-year-old Nadal's 35th appearance in a Grand Slam quarter-final as he continues his bid to win an 18th major title. "After she was complaining, they were talking in Chinese, whatever language".
"I'm going to have to really take it to him".
"Like past year, I received the information that they can't reschedule my match on the other court because of the tickets that are presold".
She will face No. 12 Jelena Ostapenko on Thursday for a berth in the final. "I probably won't have another 6-0 set this week, so I'll enjoy this one".
(11) Angelique Kerber bt.
Djokovic, victor of three singles titles at the All England Club, will next meet Japan's 24th seed Kei Nishikori.