Johanna Konta had won her past three encounters with Venus Williams, but the veteran controlled proceedings from the baseline, taking the first set in just over half an hour.
Konta rallied and won three straight games to claim the second set but Williams responded with another double break in the third to secure victory. Williams, who has won seven Grand Slam singles titles, will take on Spain's Garbine Muguruza in the quarter-finals, after the 2016 French Open champion saw off Germany's Julia Gorges 7-5 6-4.
Elsewhere, Estonian qualifier Anett Kontaveit backed up her shock win over world number one Angelique Kerber on Wednesday by beating 16th seed Croatian Mirjana Lucic-Baroni 6-1 6-1.
Kontaveit will face sixth seed Simona Halep in the quarter-finals, after the Romanian beat Russia's Anastasia Pavlyuchenkova 6-1 4-6 6-0. Unseeded Daria Gavrilova stunned Svetlana Kuznetsova of Russia 2-6 7-5 6-4 to reach the last eight, where she will play Kiki Bertens - a 7-6 (7-3) 6-1 winner over Russia's Ekaterina Makarova.
Ukraine's Elina Svitolina beat Germany's Mona Barthel 3-6 6-0 6-0 to set up a tie with second seed Karolina Pliskova, after the Czech came through 6-1 7-5 against Switzerland's Timea Bacsinszky.
