Novak Djokovic completed a 3-6 6-4 6-1 7-5 win over Spain`s Roberto Bautista Agut, having resumed in the third set.
Andy Murray was then scheduled to take on France`s Richard Gasquet in the first of the men`s quarter-finals.
Serena through, Venus out
World number one Serena Williams looked impressive as she saw off 18th seed Svitolina in just 62 minutes, making it 18 sets in a row for the American at Roland Garros.
She will next play unseeded Yulia Putintseva of Kazakhstan, who beat Spanish 12th seed Carla Suarez Navarro 7-5 7-5.
Venus Williams did not fare as well as her sister, losing 6-2 6-4 to Swiss eighth seed Timea Bacsinszky.
Kiki Bertens of the Netherlands made it four unseeded players in the women`s quarter-finals with a 7-6 (7-4) 6-3 win over American 15th seed Madison Keys.
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