Second seed Djokovic will hope his 101st match at Wimbledon - against seventh-seeded Russian Andrey Rublev in the last eight - will mark a return to vintage form.
Rybakina, meanwhile, had an easier route into the quarter-finals after her Brazilian opponent retired with a back injury while trailing the third seed 4-1 in the first set.
"It was really unlucky for Beatriz and I hope she gets better," added Rybakina.
It was also a day to rejoice for fellow American Eubanks, who got past Tsitsipas 3-6 7-6(4) 3-6 6-4 6-4 to make the quarter-finals on his Wimbledon debut.
"I feel like I'm living a dream right now, this is absolutely insane," said Eubanks, who meets Medvedev next.
Persons:
Poland's Hubert Hurkacz, Serbia's Novak Djokovic, Hannah Mckay, Djokovic, Rybakina, Medvedev, Tsitsipas, Eubanks, Novak Djokovic, Pole Hubert Hurkacz, Elena Rybakina, Beatriz Haddad Maia, Daniil Medvedev, Czech Jiri Lehecka, Stefanos Tsitsipas, Christopher Eubanks, Holder Djokovic, Andrey Rublev, Beatriz, Jabeur, Petra Kvitova, Ekaterina Alexandrova, I'm, Sabalenka, Andreeva, Shrivathsa Sridhar, Ken Ferris
Organizations:
Lawn Tennis, Croquet Club, Serbia's Novak Djokovic REUTERS, Wimbledon, Court, Madison Keys, Thomson
Locations:
London, Britain, Czech, Moscow, Kazakh, Belarus, Russia, Ukraine, Bengaluru