With world number one Rafael Nadal waiting for the victor, Tuesday's fourth set, played in much cooler conditions than the first three the day before, turned into a mini-epic before Del Potro eventually prevailed 7-6 (1) 7-6 (5) 5-7 7-6 (5).
Del Potro was forced to finish his last-16 match against Gilles Simon on Tuesday because of fading light on Monday, but said afterwards he felt he would be in a "good condition".
Novak Djokovic won his battle to be promoted to Centre Court billing for Wednesday's quarter-finals, forcing eight-time champion Roger Federer off the sport's most famous arena for the first time in three years.
Former world number one Djokovic has a 13-2 winning record against the Japanese player. So, too, is 19-year-old Denis Shapovalov of Canada.
Williams lifted her intensity and avoided facing any break points as she secured one break of her own to take the set 6-3.
"I feel like these streaks just happen", Federer said.
By contrast, eight-time champion Federer, and Nadal, the title victor on two occasions, have played exclusively on the 15,000-seater Centre Court.
The ICC shared an image of the Test rankings for batsmen which showed the 20-time Grand Slam victor as the number one batsman in the world.
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.
Cibulkova overcame a delay caused by a controversial decision from the umpire to advance to the quarterfinals with a 6-4, 6-1 victory over Hsieh Su-Wei.
Rafael Nadal is in the quarterfinals at Wimbledon for the first time since 2011.
The All England Club has come under increasing pressure to rethink its 2pm (1300GMT) start time for Sunday's men's singles final with the football showpiece in Moscow kicking off at 4pm in the United Kingdom (1500GMT). The grass isn't as slick as usual, the ball is bouncing higher, making the playing conditions more to Nadal's liking.
"It was ridiculous what happened there". "After she was complaining, they were talking in Chinese, whatever language".
The Serb, understandably miffed, revealed: "I heard that the organisers were planning to cancel my match if [Gaël] Monfils and Anderson went to a fifth [it was concluded in Anderson's favour]". But from what I've seen from him in the last couple of days, he looks like he's playing really, really well.
Latvian 12th seed Ostapenko enjoyed a 7-6 (7/4), 6-0 win against Belarusian world number 50 Aliaksandra Sasnovich.
Two-time Grand Slam champion Angelique Kerber is taking on Russian Daria Kasatkina on Centre Court.
Beaten by Serena in the 2016 final, Kerber takes on Russian 14th seed Daria Kasatkina, a 6-7 (6/8), 6-3, 6-2 victor against Belgian world number 47 Alison Van Uytvanck.