Latvia’s Sevastova, the 2016 runner-up, defeated her Dutch opponent 6-1 7-5 in one hour and 23 minutes.
Also advancing into the last eight were second-seeded home favourite Mihaela Buzarnescu and Slovakian eighth seed Polona Hercog as they saw off Tamara Zidansek 6-3 7-5 and Irina Bara 7-5 6-2 respectively.
But seventh seed Pauline Parmentier exited, the Frenchwoman retiring when 7-6 (7-0) 3-0 down against Yafan Wang.
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At the Ladies Championships in Gstaad, Sweden’s second-seeded Johanna Larsson posted a 6-4 6-1 first-round win over Leonie Kung, the 17-year-old Swiss wildcard who was the beaten finalist in the Wimbledon junior competition last week.
Meanwhile, there was elimination for this tournament’s seventh seed, with Kung’s compatriot Stefanie Voegele suffering a 6-2 6-0 round one defeat against Tamara Korpatsch of Germany.
Marketa Vondrousova and Evgeniya Rodina will meet in the quarter-finals after the former beat Elitsa Kostova and the latter Mona Barthel.
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