Kerber will play No. 14-seeded Daria Kasatkina in Tuesday’s quarterfinals.
In the men’s tournament, Roger Federer advanced to a record-extending 16th Wimbledon quarterfinal with a 6-0, 7-5, 6-4 victory over Adrian Mannarino of France.
Federer, an eight-time champion here, lost only five points in a 16-minute first set but faced break points for the first time in this year’s tournament, saving all four. Federer has now won 32 consecutive sets at Wimbledon to move within one straight-sets victory of breaking his previous longest streak at the All England Club, when he won 34 in a row between the third round in 2005 and the final in 2006.
Ninth-seeded John Isner, No. 13 Milos Raonic of Canada and No. 24 Kei Nishikori of Japan also advanced. Isner and Nishikori are in the Wimbledon quarterfinals for the first time in their careers.
Isner rode his big serve to beat the Greek teenager Stefanos Tsitsipas, 6-4, 7-6 (8), 7-6 (4). He next faces Raonic, who defeated Mackenzie McDonald, 6-3, 6-4, 6-7 (5), 6-2.
Bertens hit seven aces and saved eight of the 10 break points she faced to win 6-3, 7-6 (2) against Pliskova and complete the latest upset in the women’s draw. Bertens beat the ninth-seeded Venus Williams in the third round after coming from a break down in the third set.
Bertens next faces 13th-seeded Julia Görges, who beat Donna Vekic of Croatia, 6-3, 6-2, to secure her first Grand Slam quarterfinal appearance.
Jelena Ostapenko and Dominika Cibulkova will also meet in Tuesday’s quarterfinals.
Ostapenko reached the last eight for the second straight year with a 7-6 (4), 6-0 victory over Aliaksandra Sasnovich, while Cibulkova beat Hsieh Su-wei, 6-4, 6-1.