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World number two Kontaveit recorded a 6-3 6-2 victory over Peterson on the clay in Germany, setting up a last-eight meeting with eighth seed Andrea Petkovic.
The Estonian's win was her third over Peterson and maintained her 100 per cent career record against Swedish opponents, taking her to seven such successes.
Kontaveit was joined in the quarter-finals by fellow seeds Aliaksandra Sasnovich, who beat Aleksandra Krunic 6-3 6-2, and Maryna Zanevska, who downed Alexandra Cadantu-Ignatik 6-4 6-1.
They will face off for a semi-final spot on Thursday, while Anastasia Potapova will meet 2021 French Open champion Barbora Krejcikova after beating Maria Carle in straight sets.
At the Palermo Ladies Open, meanwhile, third seed Zhang withdrew from her last-16 clash with home favourite Jasmine Paolini before taking to the court, citing an unspecified injury.
Fellow seeds Sara Sorribes Tormo and Anna Bondar both reached the quarter-finals with straight-sets wins, however, with the pair set to face off for a semi-final berth on Friday.
