Top seed Lucie Safarova moved into the Coupe Banque Nationale quarter-finals and she was joined by Alison Van Uytvanck.
Safarova eased into the last eight with a 6-4 6-3 win over American teenager Sofia Kenin in Quebec City on Thursday.
A finalist in Budapest this year, Safarova stayed on track for her eighth WTA Tour title and first since April last year after firing down 11 aces.
Standing in the way of Safarova and a semi-final berth is fellow Czech Lucie Hradecka, who ousted Canadian hopeful Bianca Andreescu 2-6 6-2 7-5.
Belgian seventh seed Van Uytvanck saw off Marina Erakovic 6-4 7-6 (7-4) to reach the quarters of the tournament for a second successive year.
"I think it's a pretty good win, Erakovic was playing really well today," Van Uytvanck - who will next play Caroline Dolehide - said. "I played her a couple of weeks ago on grass, but I thought she definitely improved her game a lot, so for me it was tough."
Meanwhile, eighth seed Viktorija Golubic was ousted 2-6 6-3 6-4 by Sachia Vickery.