Arruabarrena won six of eight break points. She will next face Patricia Maria Tig, who beat Sara Sorribes Tormo 7-6 (2), 2-6, 6-3.
Third-seeded Zhang Shuai of China also advanced, defeating Camila Giorgi of Italy 6-2, 6-4. Giorgi had eight double-faults.
Zhang, who is bidding for her second WTA singles title, is the highest seeded player remaining. Top-seeded and defending champion Irina-Camelia Begu was eliminated on Thursday.