Third seed Bencic needed just 88 minutes to see off her 36th-ranked opponent as she made it 15 victories from her past 18 matches.
Czech wildcard Tereza Martincova is also through to the last eight on home soil after battling past French Open finalist Anastasia Pavlyuchenkova 7-6 (7-5) 7-6 (8-6).
Martincova is into her fifth quarter-final of the season and will take on number four seed Maria Sakkari, who saw off Jelena Ostapenko 6-4 6-2 earlier on Thursday.
Also through to round three is Elena Rybakina following a hard-fought 6-3 2-6 6-1 win over qualifier Magda Linette, while Jil Teichmann – who shocked former world number one Angelique Kerber in the previous round – advanced in three sets against Alison Riske.
She will face Petra Kvitova for a place in the semi-finals.