The first to advance to the semis was Coco Vandeweghe, getting past top seed and world No.1 Simona Halep in straight sets, followed by sixth seed Caroline Garcia, who enjoyed a comeback win over third seed Elina Svitolina.
Anett Kontaveit won an intense match against Anastasia Pavlyuchenkova, while fifth seed Karolina Pliskova fought past fourth seed Jelena Ostapenko in a battle that ended after midnight.
MORE PHOTOS FROM THE 2018 PORSCHE TENNIS GRAND PRIX: